Pinchas ben Elozar ben Aharon HaKohen heishiv es chamasi me'al B'nei Yisroel b'kano es kinasi b'socham (25:11)

At the end of last week's parsha, the Jewish people were enticed to sin with Midianite women, which resulted in a plague striking the nation and killing 24,000 Jews. Anxious to stem the spread of the plague, Aharon's grandson Pinchas killed Zimri, the leader of the tribe of Shimon who was publicly taking part in the sin. Parshas Pinchas begins with Hashem extolling Pinchas for his actions and promising him a covenant of peace and eternal priesthood as his reward. Interestingly, as Pinchas is singled out for praise, the letter é in his name is written smaller than usual. What is the reason for this anomaly? In his work Oznayim L'Torah, Rav Zalman Sorotzkin explains by questioning why Pinchas deserved a reward altogether in light of the fact that his grandfather Aharon acted similarly to stop a plague (Bamidbar 17:11-15) but received nothing in return, nor was Moshe rewarded on any of the numerous occasions when he interceded to protect the Jewish people. Rav Sorotzkin explains that Pinchas's action was fundamentally different in the sense that Moshe and Aharon were national leaders who bore the responsibility to care for the people and intervene on their behalf in times of crisis.

On the other hand, Pinchas, in spite of his distinguished lineage, was essentially a commoner at the time of this incident. He saw Moshe standing by idly as Zimri began to sin, and he could have easily justified remaining passive as well. Instead, Pinchas understood what the situation called for, and took it upon himself to step forward and do it himself. In commending Pinchas for his actions, the Torah therefore writes the letter é in his name smaller than usual to allude to the fact that at the time of this episode, Pinchas was a small and relatively unknown individual, and it was precisely because of his willingness to take the initiative and act big when the situation required it that he was singled out for such unprecedented accolades and reward.

Many of us can identify with Pinchas in this regard, as we too often feel small and insignificant, and even if we notice an injustice being done or a situation that calls for our involvement, we question what somebody of our lowly stature could possibly accomplish by speaking up. At such times, we should recall the tremendous praise that Pinchas received specifically because of his anonymity, which should inspire and strengthen us to take appropriate action whenever a situation warrants it.

Ach b'goral yeichalek es ha'aretz (26:55)

The Torah specifies that the land of Israel be divided among the tribes through a process of drawing lots. Rashi explains that the names of the tribes were written on 12 pieces of paper, and the boundaries of each of the twelve portions of the land were written on 12 other pieces of paper, and all 24 papers were mixed up and placed in a box. The lottery itself was conducted through Divine Inspiration by Elozar and the princes of each of the tribes. Elozar wore the Priestly garments, including the Urim V'Tumim, and announced that if the name of a certain tribe was drawn, these would be the borders of the corresponding portion of land. The leader of the tribe mentioned by Elozar would then select two pieces of paper from the box, and in each case, one of the papers he selected contained the name of his tribe, and the other paper contained the region specified by Elozar. The reason for apportioning the land in this manner was to prevent discord among the tribes by making it clear that the resulting division of land was Hashem's will. In order to understand just how convincing and persuasive this miracle was, it would be helpful to appreciate just how unlikely it was to have happened by chance.

In order to calculate the likelihood of this outcome occurring naturally, we must determine the odds of each tribal leader selecting both the name of his tribe and also the portion of land that was specified by Elozar. The first tribal prince who was called chose two pieces of paper from among the 24 that were contained in the box. The probability of correctly selecting the first paper is 1/24, and the odds of accurately taking the second one are 1/23. However, because there was no requirement to select the name of the tribe first and the portion of land afterward, the order in which he chose the two pieces of paper was irrelevant. Since Elozar's prediction was fulfilled whether he first chose the name of his tribe and then the corresponding section of land or vice-versa, the odds of the first tribal leader successfully choosing the correct pieces of paper is 2/(24*23).

When the second tribal prince comes forward for his turn, there are only 22 pieces of paper remaining in the box, so the probability of him correctly taking the two pieces predicted by Elozar is 2/ (22*21). This will continue until the last leader, whose odds will be 2/(2*1), which is 1, since the only two remaining pieces of paper in the box belong to his tribe, and his success is therefore guaranteed. In order to calculate the likelihood of all 12 tribal leaders choosing correctly, we must multiply each individual leader's odds together, which yields a probability of success of 212/(24*23*22*21*…*2*1). The denominator can also be more succinctly written as 24!, so the odds of success can be expressed as 212 / 24!, which when calculated reveals that the odds of this lottery system working out exactly as Elozar predicted by random chance is approximately 1 in 151,476,000,000,000,000,000.

This calculation is based on the explanation given by Rashi in his commentary on Chumash. However, his grandson, the Rashbam, writes in his commentary on the Gemora (Bava Basra 122a) that two boxes were used. One box contained 12 pieces of paper on which were written the names of the tribes, and the other box contained 12 pieces of paper on which were written the boundaries of the respective portions of the land. When it was his turn, each tribal prince selected one piece of paper from each of the two boxes.

This explanation alters the calculation of the likelihood of random success, as the first leader now has a 1/12 probability of choosing the name of his tribe from the first box, and a 1/12 probability of selecting the area of land predicted by Elozar. As a result, the odds of success for the first tribal prince are 1/122, while the probability of the second leader choosing correctly are 1/112, which is continued all the way until the final leader, whose odds are 1/112, which is 1, since his success is guaranteed. Multiplying the odds of all of the leaders together, the likelihood of Elozar's predictions being randomly fulfilled in this model is 1/(122*112*102…*22*12). This can also be expressed as 1/(12! 2), and when calculated yields a probability of random success of 1 in 229,442,532,802,560,000, which is approximately 660 times more likely than the odds according to the explanation given by Rashi in his commentary on Chumash.

To appreciate the sheer magnitude of how improbable this would be, the odds of winning $1,000,000 in the New York Mega Millions lottery are approximately 1 in 18 million, which is more than 12 billion times more likely than the successful fulfillment of all of Elozar's predictions according to the Rashbam's commentary on the Gemora, and a whopping eight trillion times more probable according to Rashi's commentary on Chumash. It would actually be more likely to win the lottery twice in one week than for the tribal lottery to occur according to random chance, which gives us a newfound appreciation of the extent of the miracle that Hashem performed in dividing Eretz Yisroel among the tribes.

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Parsha Points to Ponder (and sources which discuss them):

1) Rashi writes (25:13) that prior to the episode in which he killed Zimri and Cozbi, Pinchas wasn't a Kohen. As he was alive at the time that Aharon and his sons were anointed, why didn't Hashem allow him to become a Kohen at that time? (Gur Aryeh, Sifsei Chochomim, Ohr Gedalyahu)

2) Rashi writes (26:1) that just as Moshe began his leadership of the Jewish nation by counting them after the exodus from Egypt, so too he was commanded to count them at the end of his leadership as the time of his death approached. After the sin of the golden calf, the male Jews between ages 20 and 60 numbered 603,550 (Shemos 38:26), while 39 years later they numbered only 601,730 (26:51). In what way is it considered a compliment to Moshe that the total number of Jews actually decreased during the period of his leadership? (Darash Moshe)

3) Does a firstborn son delivered through Caesarian-section receive a double portion in the inheritance of his father, and if he does not, does the son who is born after him receive a double portion instead? (Rambam Hilchos Nachalos 2:11)

4) In Parshas Emor (Vayikra 23:24), the Torah refers to Rosh Hashana as zichron teruah - a remembrance of shofar blasts. In Parshas Pinchas (29:1), it is called yom teruah - a day of shofar blowing. The Gemora in Rosh Hashana (29b) explains that Parshas Emor refers to Rosh Hashana which falls on Shabbos, in which case the shofar is only remembered but not actually blown, and our parsha refers to Rosh Hashana which falls during the week, when the shofar is sounded. Why did the Torah write them in this order, first mentioning the less common case of Rosh Hashana falling on Shabbos? (Rav Akiva Eiger Al HaTorah, Peninim MiShulchan Gevoha Parshas Emor)

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