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Permutations and Combinations

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Question : 36 of 56

Marks: +1, -0

n+2 C_{n}=45

find the value of

n

7
8
9
6

Solution:

Concept:

Use the property of combinations:

\binom{n+2}{n} = \binom{n+2}{2}

.

Explanation:

Given

\binom{n+2}{n} = 45

.

Since

\binom{n+2}{n} = \binom{n+2}{2}

, we have

\frac{(n+2)(n+1)}{2} = 45

.

Multiply both sides by 2:

(n+2)(n+1) = 90

.

Expand:

n^2 + 3n + 2 = 90

, so

n^2 + 3n - 88 = 0

.

Factor:

(n+11)(n-8) = 0

.

Thus

n = 8

(reject

n = -11

as

n

is positive).

Answer:

n = 8

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