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

$35 w a y s$ $35ways$

This is permutation, hence;

$^{n} P_{r} = \frac{n!}{(n - r) r!}$ $""^nP_r = (n!)/((n - r)r!)$

Where;

$n = 7$ $n = 7$

$r = 4$ $r = 4$

Substituting..

$^{7} P_{4} = \frac{7!}{(7 - 4) 4!}$ $""^7P_4 = (7!)/((7 - 4)4!)$

$^{7} P_{4} = \frac{7!}{3! 4!}$ $""^7P_4 = (7!)/(3!4!)$

$^{7} P_{4} = \frac{7 \times 6 \times 5 \times 4!}{3! 4!}$ $""^7P_4 = (7 xx 6 xx 5 xx 4!)/(3!4!)$

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

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

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

$""^7P_4 = 210/6$

$""^7P_4 = 35ways$