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?

Guest Nov 27, 2021

#1**+1 **

The probability that all 6 are hazelnuts is: [ _{9}C_{6} ·_{10}C_{0} · _{5}C_{0} ] / _{24}C_{6}

(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: [ _{9}C_{0} ·_{10}C_{6} · _{5}C_{0} ] / _{24}C_{6}

(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.

geno3141 Nov 27, 2021