Question

How many subsets of three elements each can be made from a set of five elements?

A)10
B)20
C)60

Answer 1

the CORRECT answer should be 10, because if you take 5!/3!*(5-3)! it equals 10

Answer 2

Answer:  The correct option is (A) 10.

Step-by-step explanation:  We are given to find the number of subsets of three elements each can be made from a set of five elements.

Since we have five elements, out of which we are to select three.

So, the number of subsets will be given by the combination of five elements taking three at a time.

The combinations of 'n' elements taking 'r' (r is less than or equal to n) at a time is given by the formula:

$^nC_r=\dfrac{n!}{r!(n-r)!}.$

Here, n = 5  and  r = 3.

Therefore, the total number of subsets will be

$^5C_3\\\\\\=\dfrac{5!}{3!(5-3)!}\\\\\\=\dfrac{5!}{3!2!}\\\\\\=\dfrac{5\times 4\times 3!}{3!\times2\times1}\\\\\\=5\times2\\\\=10.$

Thus, the required number of subsets is 10.

Option (A) is correct.