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anayajae24

26.12.2020

Mathematics

The combination formula is given by

nCr = $\frac{n!}{r!(n-r)!}$

₁₀C₄ = $\frac{10!}{4!(10-4)!}$

= $\frac{10!}{4!(6)!}$

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

= $\frac{10X9X8X7X6X5X4X3X2X1}{4!(6X5X4X3X2X1)}$

= $\frac{10X9X8X7}{4!}$

= $\frac{10X9X8X7}{4X3X2X1}$

= $\frac{5040}{24}$

= 210

₄C₂ = $\frac{4!}{2!(4-2)!}$

= $\frac{4X3X2X1}{2!(2!)}$

= $\frac{24}{4}$

So we have

₁₀C₄ .₄C₂ = 210 x 6 = 1260

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