A Combination Problem

Probability Level 2

If you choose 3 student out of 100 students to go to Singapore, how many combination can you make?


The answer is 161700.

Isabella Yan by Isabella Yan , 19, China

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2 solutions

Mahdi Raza
Jan 11, 2020

There are 100 students and you want to choose 3 of them. The problem is simply asking out of 100 chose 3, which is equivalent to:

( 100 3 ) 100\choose 3 = 100 ! 3 ! ⋅ 97 ! \frac{100!}{3!\cdot97!} = 100 ⋅ 99 ⋅ 98 ⋅ 97 ! 3 ! ⋅ 97 ! \frac{100\cdot99\cdot98\cdot97!}{3!\cdot97!} = 100 ⋅ 99 ⋅ 98 ⋅ 97 ! 3 ! ⋅ 97 ! \frac{100\cdot99\cdot98\cdot\cancel{97!}}{3!\cdot\cancel{97!}} = 970200 6 \frac{970200}{6} = 161700 161700

1 Helpful 0 Interesting 1 Brilliant 0 Confused
Isabella Yan
Mar 2, 2015

100C3=161700

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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