The combination formula is given by
nCr = [tex] \frac{n!}{r!(n-r)!} [/tex]
₁₀C₄ = [tex] \frac{10!}{4!(10-4)!} [/tex]
= [tex] \frac{10!}{4!(6)!} [/tex]
when you are not using a calculator, you can cancel out similar terms by expanding the factorials
= [tex] \frac{10X9X8X7X6X5X4X3X2X1}{4!(6X5X4X3X2X1)} [/tex]
= [tex] \frac{10X9X8X7}{4!} [/tex]
=[tex] \frac{10X9X8X7}{4X3X2X1} [/tex]
=[tex] \frac{5040}{24} [/tex]
= 210
₄C₂ = [tex] \frac{4!}{2!(4-2)!} [/tex]
= [tex] \frac{4X3X2X1}{2!(2!)} [/tex]
= [tex] \frac{24}{4} [/tex]
=6
So we have
₁₀C₄ .₄C₂ = 210 x 6 = 1260
