Ally J.
asked • 05/04/21Permutations Help
A salesperson needs to visit 15
different offices during the week.
c) In how many ways could she visit three
different offices each day from Monday
to Friday?
I thought of it as 1st day 15x14x13, 2nd day 12x11x10, 3rd day 9x8x7.....until Friday.
Please explain how to do this question?
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1 Expert Answer
Mike D. answered • 05/04/21
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You can choose the Monday offices in C (15,3) ways
Having chosen those , on Tuesday she can choose C (12,3)
Wednesday C (9,3)
Thursday C (6.3)
Friday C (3,3)
So C(15,3) x C (12,3) x C (9,3) x C (6,3) x C(3,3)
= 455 x 220 x 84 x 20 x 1 = 168, 168, 000 ways
Order of the offices on a specific day isn't important
Ally J.
Thank you so much for your the help, but the solution had stated that it was 13,650. Just wasn't sure how they got that.
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05/04/21
Mike D.
I don't think their solution is correct. Following your idea (which was good), you need to divide 6 x 6 x 6 x 6 x 6 because the order of offices each day doesnt matter. doing that gives 15! / 6x6x6x6x6 which gives my answer.
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05/04/21
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Michael M.
Getting the same thing Mike got. Another way you can think of it is 15! / (3! * 3! * 3! * 3! * 3!)05/04/21