Question

if 1000C98 = 999C97 + XC901 find X ​

Answer 1

=> 1000C98 = 999C97 + XC901

=> 1000C902 = 999C902 + XC901
[Because nCr = nC(n - r)]

=> X = 999
[Because nCr + nC(r + 1) = (n + 1)C(r + 1)]

So option (A) is the answer.

Plz ask me if you've any doubt on my answer.

Thank you.

Answer 2

Concept

We know the formula in the combination which is in the factorial form, i.e.

nCr + nC(r+1) = (n+1)C(r+1)....(1)

where n and r are natural numbers. Also nCr is further defined as

nCr = n!/r!(n-1)!....(2)

Also nCr = nC(n-r)....(3)

Given

The given expression is as follows,

1000C98 = 999C97 + XC901

Find

We have to calculate the value of X.

Solution

Since,

1000C98 = 999C97 + XC901

Therefore, using equation (3), we have

1000C(1000-98) = 999C(999-97) + XC901

1000C902 = 999C902 + XC901

(999+1)C(901+1) = 999C(901+1) + XC901

Therefore comparing the above equation with equation (1), we get

n = X = 999

r = 901

Therefore option A is correct.

Hence the value of X comes out to be 999, so option A is the correct.

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