Question

Evaluate the given expression. 10c4 4c2

Answer 1

The combination formula is given by

nCr =
`(n!)/(r!(n-r)!)`

₁₀C₄ =
`(10!)/(4!(10-4)!)`

=
`(10!)/(4!(6)!)`

when you are not using a calculator, you can cancel out similar terms by expanding the factorials

=
`(10X9X8X7X6X5X4X3X2X1)/(4!(6X5X4X3X2X1))`

=
`(10X9X8X7)/(4!)`

=
`(10X9X8X7)/(4X3X2X1)`

=
`(5040)/(24)`

= 210

₄C₂ =
`(4!)/(2!(4-2)!)`

=
`(4X3X2X1)/(2!(2!))`

=
`(24)/(4)`

=6

So we have

₁₀C₄ .₄C₂ = 210 x 6 = 1260