A bag contains 9 hazelnuts, 10 almonds and 5 walnuts. If 6 are drawn at random, what is the probability all six will be the same nut?
The probability that all 6 are hazelnuts is: [ 9C6 ·10C0 · 5C0 ] / 24C6
(found by choosing 6 of the 9 hazelnuts, 0 of the 10 almonds, and 0 of the 5 walnuts; divided by the
number of ways to choose a set of 6 from a set of 24)
The probability that all 6 are almonds is: [ 9C0 ·10C6 · 5C0 ] / 24C6
(found by choosing 0 of the 9 hazelnuts, 6 of the 10 almonds, and 0 of the 5 walnuts; divided by the
number of ways to choose a set of 6 from a set of 24)
The probability that all 6 are walnuts is: 0 (because there aren't 6 of them.
To find the final probability add the above two probabilities.