Question

1.IfnC,-"C2, find nC..

Answer 1

The given equation is C n 8 = C n 2 .

The formula for the condition C n a = C n b is,

n=a+b

Substitute 8 for a and 2 for b in the above condition.

n=8+2 =10

Since the value of n comes out to be 10, then the term C n 2 is written as C 10 2 .

The formula to calculate the combination is defined as,

C n r = n! ( n−r )!r!

Substitute 10 for n and 2 for r in the above formula.

C 10 2 = 10! ( 10−2 )!2! = 10! 8!2!

Cancel the common factors by factorizing the bigger term to the factorial.

The formula to calculate the factors of a factorial in terms of factorial itself is,

n!=n( n−1 )! n!=n( n−1 )( n−2 )!                 [ n≥2 ] ⋮

The combination becomes,

C 10 2 = 10×9×8! 8!2×1 = 10×9 2 =45

Thus, the value of C 10 2 is 45.