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# From her collection of 9 different hats, Ellen wants to wear one diffe

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Math Expert
Joined: 02 Sep 2009
Posts: 51223
From her collection of 9 different hats, Ellen wants to wear one diffe  [#permalink]

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13 Apr 2018, 01:50
00:00

Difficulty:

25% (medium)

Question Stats:

82% (01:12) correct 18% (01:44) wrong based on 86 sessions

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From her collection of 9 different hats, Ellen wants to wear one different hat to school each day during a four-day week. How many different sequences of hats could she wear?

A. 9
B. 54
C. 1068
D. 2126
E. 3024

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Joined: 04 Apr 2018
Posts: 21
Re: From her collection of 9 different hats, Ellen wants to wear one diffe  [#permalink]

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13 Apr 2018, 03:37
1
Ellen has 9 choices to wear on 1st day but only 8 on 2nd day, 7 choices on 3rd day & 6 choices on 4th day.
Hence the no. of ways = 9*8*7*6 = 3024, option E. 3024
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Re: From her collection of 9 different hats, Ellen wants to wear one diffe  [#permalink]

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16 Apr 2018, 16:11
Bunuel wrote:
From her collection of 9 different hats, Ellen wants to wear one different hat to school each day during a four-day week. How many different sequences of hats could she wear?

A. 9
B. 54
C. 1068
D. 2126
E. 3024

On the first day, Ellen can choose from any of the 9 hats; on the second day, she can choose any hat except the one she wore on the previous day, so she can choose from 8 hats. Similarly, on day 3, she can choose from any of the 7 remaining hats, and on day 4 she can choose from 6 hats.

Thus, Ellen can wear 9 x 8 x 7 x 6 = 3,024 different combinations of her hats.

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Re: From her collection of 9 different hats, Ellen wants to wear one diffe  [#permalink]

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28 Apr 2018, 09:11
Same hat will not repeat so
9*8*7*6=3024

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Joined: 01 Jun 2015
Posts: 42
Location: India
Re: From her collection of 9 different hats, Ellen wants to wear one diffe  [#permalink]

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28 Apr 2018, 10:30
9 hats available. 4 days different hat required.

So 1st day we can any one from 9, 2nd day any one from 8 , 3rd day any one from 7 and 4th day any one from 6

9*8*7*6
Re: From her collection of 9 different hats, Ellen wants to wear one diffe &nbs [#permalink] 28 Apr 2018, 10:30
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