Question

Dean mixed together different kind of nuts as a snack. There were 9 nuts in the bowl, 7 of

which were hazelnuts.
If Dean randomly chose to eat 6 of the nuts, what is the probability that all of them are
hazelnuts?
Write your answer as a decimal rounded to four decimal places.

Answer 1

0.0833

Explanation:

There are 7C6 = 7 ways to choose 6 hazelnuts from the 7 present.

There are 9C6 = 84 ways to choose 6 nuts from the 9 present.

The probability of choosing 6 hazelnuts from the 9 present is ...

7/84 = 1/12 = 0.0833...(repeating)

The probability of interest is 0.0833.

____

Comment on the notation

The notation nCk means n!/(k!(n-k)!). It is the number of ways k items can be chosen from n items without regard to order. It can be pronounced "n choose k."