Question

A person eating at a cafeteria must choose 3 of the 14 vegetables on offer. Calculate the number of elements in the sample space for this experiment

a)990
b) 0165
c) 1092
d) 2184
e)364
f)None of the above

Answer 1

The sample space for choosing 3 vegetables out of 14 is 2184.

Step-by-step explanation:

The sample space for choosing 3 vegetables out of 14 is calculated using the combination formula. The formula for combination is C(n, r) = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices. In this case, n = 14 and r = 3.

So, the number of elements in the sample space is:

C(14, 3) = 14! / (3!(14-3)!) = 14! / (3!11!) = (14 * 13 * 12) / (3 * 2 * 1) = 2184.

Therefore, the correct answer is d) 2184.