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:5

Step-by-step explanation:

now i shall say What you are looking for are binomial coefficient Those represent how many subset of size certain(x) you can choose among  certain (y)possibilities.

According to the formula, you need to solve :

n!2!(n−2)!=10  

It could be pretty hard to solve at first but let’s decompose it.

n!(n−2)!=2!×10=20  

Note that :  n!(n−k)!=(n−k+1)×(n−k+2)…×(n−1)×n  

So you are looking for something like : (5–2+1)×(5–2+2)×…×n=20  

4×5×…×n=20  

Clearly,  n=5  

For bigger numbers you can use sum of geometric suites to solve.