Question

A person eating at a cafeteria must choose 3 of the 15 vegetables on offer. Calculate the number of elements in the sample space for this experiment.

a) 2730
b) 220
c) 1365
d) 455
e ) 1320
f) None of the above

Answer 1

The number of ways to choose 3 vegetables out of 15 is calculated using the combination formula. It results in 455 different combinations, making the correct answer d) 455.

Step-by-step explanation:

The student is tasked with choosing 3 vegetables out of 15 different options available in a cafeteria, without considering order and without replacement. The number of ways to do this is calculated using the combination formula C(n, k) = n! / (k! * (n-k)!), where ‘n’ is the total number of items to choose from, and ‘k’ is the number of items to choose.

Here, n=15 and k=3. Plugging these into the formula gives us:

C(15, 3) = 15! / (3! * (15-3)!)

= 15! / (3! *12!)

= (15 × 14 × 13) / (3 × 2 × 1)

= 455

Therefore, the correct answer is d) 455, indicating the number of possible combinations for choosing 3 vegetables from the 15 on offer.