Six students are asked to secretly choose a number from 1 to 15. Determine the probability that at least two students choose the same number

Answer:

Six students are asked to secretly choose a number from 1 to 15. The probability that at least two students choose the same number is 1 - probability that none of the students choose the same number.

The number of ways in which the numbers can be chosen is 15^6. The number of ways in which each student choses a unique number is 15*14*13*12*11*10. This gives a probbaility of [(15*14*13*12*11*10)/15^6]

[1 - (15*14*13*12*11*10)/15^6]

[~~ 0.6836]

The required probability is approximately 0.6836