Question

If the number of subsets with two elements of a set p is 10 then find the total number of elements is in cpp

Answer 1

Answer:

number of subset of with 2 element nc2

then nc2=10     now n(n-1)÷2=10

n(n-1)=20      then n(n-1)=5(5-1)

therefore n=5

Step-by-step explanation:

Answer 2

Answer:

The number of elements in set P would be 5.

Step-by-step explanation:

Suppose the number of elements in set P is n,

Since, the number of subsets of P having two elements is,

$^nC_2$

According to the question,

$^nC_2 = 10$

$\frac{n!}{2!(n-2)!} = 10$

$\frac{n(n-1)}{2}=10$

$n^2 - n = 20$

$n^2 - n - 20 = 0$

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

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

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

⇒ n = -4( not possible ) or 5,

Hence, the number of elements in set P would be 5.