Question

Find 'n' if:

P(n, 2) = 110.
P(n, n) = 5040.
C(n, 2) = 45.
C(n, 5) = C(n, 2).
a) 10
b) 7
c) 8
d) 9

Answer 1

To find the value of 'n', solve the equation P(n, 2) = 110 by using the formula for permutations. The value of 'n' is 11.

Step-by-step explanation:

To find the value of 'n', first let's consider the equation P(n, 2) = 110. P(n, k) represents the number of permutations of n objects taken k at a time. So, P(n, 2) means we are finding the number of permutations of n objects taken 2 at a time. Given that P(n, 2) = 110, we need to find the value of 'n'.

We know that P(n, 2) = n!/(n-2)!. Simplifying this equation, we have n*(n-1) = 110. By solving this equation, we find that n = 11 or n = -10. However, since 'n' represents the number of objects, it cannot be negative. Therefore, the value of 'n' is 11.