Question

If the number of subsets with two

elements of a set P is 10, then find the

total number of elements in the set P​

Answer 1

Answer:

given. number of subsets with two elements is 10.

suppose there are n elements in the set P.

since, order of elements in a subset doesn't matter, it is basically selection of two elements out of n elements which is given by nC2

so, nC2 = 10

n(n-1)/2 = 10

n^2 - n - 20 = 0

n^2 - 5n + 4n - 20 = 0

n(n-5) + 4(n-5) = 0

(n-5) ( n+4) = 0

n = -4, 5

negative number is not possible

so n = 5