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# In how many ways can letters of word ASSISTANT be arranged?

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Joined: 18 Dec 2017
Posts: 819
Location: United States (KS)
In how many ways can letters of word ASSISTANT be arranged?  [#permalink]

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22 Nov 2019, 09:12
1
1
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Difficulty:

35% (medium)

Question Stats:

72% (01:41) correct 28% (01:45) wrong based on 18 sessions

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Question: In how many ways can letters of word ASSISTANT be arranged?

A. 13600
B. 5040
C. 30240
D. 15120
E. 22680

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Re: In how many ways can letters of word ASSISTANT be arranged?  [#permalink]

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22 Nov 2019, 09:49
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Top Contributor
TheNightKing wrote:
Question: In how many ways can letters of word ASSISTANT be arranged?

A. 13600
B. 5040
C. 30240
D. 15120
E. 22680

--------------ASIDE-------------------------
When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:

If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]

So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are 11 letters in total
There are 4 identical I's
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]
-----------------------------------

Onto the question!

In ASSISTANT:
There are 9 letters in total
There are 3 identical S's
There are 2 identical A's
There are 2 identical T's
So, the total number of possible arrangements = 9!/[(3!)(2!)(2!)]
= (9)(8)(7)(6)(5)(4)(3)(2)(1)/(3)(2)(1)(2)(1)(2)(1)
= (9)(8)(7)(6)(5)(4)/(2)(1)(2)(1)
= (9)(8)(7)(6)(5)(4)/(2)(1)(2)(1)
= (9)(8)(7)(6)(5)
= 15,120

Cheers,
Brent
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Re: In how many ways can letters of word ASSISTANT be arranged?  [#permalink]

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22 Nov 2019, 10:31
TheNightKing wrote:
Question: In how many ways can letters of word ASSISTANT be arranged?

A. 13600
B. 5040
C. 30240
D. 15120
E. 22680

ASSISTANT = 9!/(2!*3!*2! )
solve = 15120
IMO D
Re: In how many ways can letters of word ASSISTANT be arranged?   [#permalink] 22 Nov 2019, 10:31
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# In how many ways can letters of word ASSISTANT be arranged?

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