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Pascal Triangle

If n C 4= n C...

Question

If $^{n} C_{4} =^{n} C_{5}$ , then the value of $^{n} C_{2}$ is

A

10

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B

28

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C

21

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D

36

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Solution

The correct option is D $36$
As $^{n} C_{4} =^{n} C_{5}$ , so
$n = 4 + 5 = 9$
Now,
$^{9} C_{2} = \frac{9!}{7! 2!} = \frac{9 \times 8}{2} = 36$

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Similar questions

a =^{n} C_{0} +^{n} C_{3} +^{n} C_{6} + . . .

b =^{n} C_{1} +^{n} C_{2} +^{n} C_{4} +^{n} C_{5} +^{n} C_{7} +^{n} C_{8} + . . .

c =^{n} C_{1} -^{n} C_{2} +^{n} C_{4} -^{n} C_{5} +^{n} C_{7} -^{n} C_{8} + . . .

,
then the value of

{(a - \frac{b}{2})}^{2} + \frac{3 c^{2}}{4}

a =^{n} C_{0} +^{n} C_{3} +^{n} C_{6} + . . .

b =^{n} C_{1} +^{n} C_{2} +^{n} C_{4} +^{n} C_{5} +^{n} C_{7} +^{n} C_{8} + . . .

c =^{n} C_{1} -^{n} C_{2} +^{n} C_{4} -^{n} C_{5} +^{n} C_{7} -^{n} C_{8} + . . .

,
then the value of

{(a - \frac{b}{2})}^{2} + \frac{3 c^{2}}{4}

If $^{n} P_{4}$ = 24, $^{n} C_{5}$ , then the value of n is

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Pascal Triangle

Standard XII Mathematics

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