Permutations - Selecting and ordering (two actions)
Combunations - Selecting (one action)
n!/r!(n-r)!
Ex.
10C5
1st step: Just like Permutation find n and r and arrange according to the formula
n=10
r=5
10!/5!(10-5)!
2nd step: Substract (n-r)!
10!/5!5!
3rd step: Evaluate
10*9*8*7*6*5!/5!5! -> cancel one 5! in numerator and denominator
4th step : simplify
10*9*8*7*6/5! --> 30240/120 = {252}
252 is the final answer
Ex. 2
A class that consists of 24 boys and 15 girls. Class committee must consists 10 students. How many ways can this be done if, there are to be 7 boys and 4 girls in this class committee
Calculate:
Formula: Boys * Girls
Boys
24C7
24!/7!(24-7)!
24!/7!17!
24*23*22*21*20*19*18*17/7!17!--->24*23*22*21*20*19*18/7!
1,744,364,160/7!
=364,104
Girls
15C4
15!/4!(15-4)!
15!/4!11!
15*14*13*12*11!/4!11!--->15*14*13*12/4!
32760/4!
=1,365
364,104*1,365 = {497,001,960}
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