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rxs0005
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How many different arrangements of letters are possible if 27 Nov 2010, 07:49
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45% (medium)

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65% (01:32) correct 35% (01:42) wrong based on 589 sessions

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How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6
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D
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Bunuel
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How many different arrangements of letters are possible if 27 Nov 2010, 07:57
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rxs0005
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6
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Since A and E must be among 3 letters then the third letter must be out of B, C and D. 3C1 = 3 ways to choose which one it'll be. Now, 3 different letters (A, E and the third one) can be arranged in 3!=6 ways, so the final answer is 3*6=18.

Answer: D.
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hirendhanak
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How many different arrangements of letters are possible if 03 Dec 2010, 04:01
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Bunuel
rxs0005
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6

As A and E must be among 3 letters than the third letter must be out of B, C and D. 3C1=3 ways to choose which one it'll be. Now, 3 different letters can be arranged in 3!=6 ways, so final answer is 3*6=18.

Answer: D.
Show more

I could understand the first part that 3C1 , why cant we have 5C2*3C1

I sometimes fail to understand the basic diff when to apply permutation and when combination ?

if you can give a brief difference... thanks in advance
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How many different arrangements of letters are possible if 03 Dec 2010, 05:10
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hirendhanak
Bunuel
rxs0005
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6

As A and E must be among 3 letters than the third letter must be out of B, C and D. 3C1=3 ways to choose which one it'll be. Now, 3 different letters can be arranged in 3!=6 ways, so final answer is 3*6=18.

Answer: D.

I could understand the first part that 3C1 , why cant we have 5C2*3C1

I sometimes fail to understand the basic diff when to apply permutation and when combination ?

if you can give a brief difference... thanks in advance
Show more

We are asked about the # of arrangements of 3 letters: {ABE} is a different arrangement from {EBA}, so for every group of 3 letters (for every selection of 3 letters) there will be 3 different arrangements possible and as there are total of 3 groups (3 selections) possible then there will be total of 3*6=18 arrangements.

Generally:
The words "Permutation" and "Arrangement" are synonymous and can be used interchangeably.
The words "Combination" and "Selection" are synonymous and can be used interchangeably.

Hope it's clear.
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How many different arrangements of letters are possible if 19 Aug 2015, 13:19
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rxs0005
How many different arrangements of letters are possible if three letters are chosen from the letters A through E and the letters E and A must be among the letters selected?

(A) 72
(B) 64
(C) 36
(D) 18
(E) 6
Show more

If one visualises this step by step:

Attachment:
STEP BY STEP.jpg
STEP BY STEP.jpg [ 12.52 KiB | Viewed 8674 times ]

With the first step you just ask yourself how many different arrangements there are of 3 Letters? As bunuel calcualted this is simply 3! = 6
Then the constraints; put everything in so called "selection-boxes" and ask yourself, how many possible combinations does the first letter have, the second, and the last if A and E must be among the selected. Finally multiply with 6.
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How many different arrangements of letters are possible if 06 Jun 2024, 20:39
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­There is an ambiguity in the question Cause nowhere does it say they A/e cannot be selected again.
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How many different arrangements of letters are possible if 24 Nov 2025, 16:14
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