Problem 5

Probability Level 1

If I were to pick 6 different numbers from 45 available numbers, how many selections are possible if the order doesn't matter?

Check out the set: Combinatorics .
5864443200 32400 270 8145060

Angela Fajardo by Angela Fajardo , 19, Philippines

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1 solution

Tapas Mazumdar
Sep 30, 2016

Relevant wiki: Combinations - Problem Solving

Ways to select 6 6 objects (here, numbers) from a selection of 45 45 objects (if order doesn't matter), is given by:

N = ( 45 6 ) = 45 ! 6 ! × 39 ! = 8145060 N = \begin{pmatrix} 45 \\ 6 \end{pmatrix} = \dfrac{45!}{6! \times 39!} = \boxed{8145060}

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