Barbara has 7 swimsuits. She needs to take 4 swimsuits on a vacation. In how many different ways can she choose 4 swimsuits out of 7?

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Answer 1 · 2018-05-31T19:47:58

#35ways#

This is permutation, hence;

#""^nP_r = (n!)/((n - r)r!)#

Where;

#n = 7#

#r = 4#

Substituting..

#""^7P_4 = (7!)/((7 - 4)4!)#

#""^7P_4 = (7!)/(3!4!)#

#""^7P_4 = (7 xx 6 xx 5 xx 4!)/(3!4!)#

#""^7P_4 = (7 xx 6 xx 5 xx cancel(4!))/(3!cancel(4!))#

#""^7P_4 = (7 xx 6 xx 5)/(3!)#

#""^7P_4 = (7 xx 6 xx 5)/(3 xx 2 xx 1)#

#""^7P_4 = 210/6#

#""^7P_4 = 35ways#