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..

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

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

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

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

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

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

$""^7P_4 = 210/6$

$""^7P_4 = 35ways$