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JAMB Mathematics 2022 Paper

Question : 29

Total: 39

Evaluate

^{n^{2}+1}

_{n+5}

if n = 3

Solution:

Concept:

Substitute the given value of

n

into the combination expression and evaluate using the factorial formula.

Explanation:

Given

n = 3

, substitute into

{^{n^{2}+1}C_{n+5}}

{^{3^{2}+1}C_{3+5}} = {^{9+1}C_{8}} = {^{10}C_{8}}

Use the combination formula:

{^{10}C_{8}} = \frac{10!}{8!(10-8)!} = \frac{10!}{8! \cdot 2!}

Expand the factorials and cancel common terms:

\frac{10 \times 9 \times 8!}{8! \times 2 \times 1} = \frac{10 \times 9}{2} = 45

Thus, the value of the expression is

45

Answer:

45

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