Question

if X={g,o,a,i,s} how many subsets of X contain exactly 3 elements

Answer 1

Answer:

Subsets of x that contain exactly 3 elements are 12.

Answer 2

Number sets contain exactly 3 elements = 10

Given: X = {g,o,a,i,s}  

To find: Number of subsets of X contains exactly 3 elements

Solution: Number of elements in X, n(X) = 5  

Number of elements that subsets must be contain = 3  

Therefore, number of subsets = ⁵C₃  

⇒  ⁵C₃  =  $\frac{5!}{(5-3)!(3!)}$  

= $\frac{5!}{2!.3!}$ = $\frac{5(4)3!}{2!.3!}$ = $\frac{20}{2}$ = 10

Number sets contain exactly 3 elements = 10

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