Combination Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
How many ways can you choose 44 books from a shelf of 1010 books?

Solution

  1. 1
    (104)=10!4!⋅6!=10×9×8×74×3×2×1\binom{10}{4} = \frac{10!}{4! \cdot 6!} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1}.
  2. 2
    =504024=210= \frac{5040}{24} = 210.

Answer

(104)=210\binom{10}{4} = 210
Since the order of selecting books does not matter, use combinations. Note that (104)=(106)\binom{10}{4} = \binom{10}{6} by symmetry.

About Combination

A combination is an unordered selection of objects — the number of ways to choose rr items from nn distinct items is C(n,r)=n!r!(n−r)!C(n,r) = \frac{n!}{r!(n-r)!}.

Learn more about Combination →

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