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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?

 Nov 27, 2021
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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.

 Nov 27, 2021

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