Solution:

Given that n1 n2p2=132 and n1-n2p2=30.

To solve this problem, we need to use the concepts of permutations and combinations.

Permutations:

A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by:

nPr = n! / (n-r)!

Combinations:

A combination is a selection of objects in which order does not matter. The number of combinations of n objects taken r at a time is given by:

nCr = n! / r! (n-r)!

Using these formulas, we can solve the given problem.

Step 1: Finding the Relation between n1 and n2

n1-n2p2=30

We know that n1 n2p2=132

Therefore, n1 = 132/n2p2

Substituting this value in the above equation, we get:

(132/n2p2) - n2p2 = 30

Simplifying this equation, we get:

132 - n2p2^2 = 30n2p2

n2p2^2 + 30n2p2 - 132 = 0

We can solve this quadratic equation to get the values of n2 and p2.

Step 2: Finding the Value of n1

Once we have the values of n2 and p2, we can substitute them in the equation n1 n2p2=132 to get the value of n1.

Step 3: Checking the Solution

We can verify our solution by checking if n1-n2p2=30. If this equation is satisfied, then our solution is correct.

Conclusion:

Thus, we have solved the given problem using the concepts of permutations and combinations. It is important to understand these concepts to solve problems related to probability and statistics.