How many different groups of three distinct letters are possible if th

Question

How many different groups of three distinct letters are possible if the three letters are chosen from the letters A, B, C, D, and E and A must be one of the letters selected?

A. 60
B. 10
C. 6
D. 4
E. 3

Chemerical71 · Answer

How many different groups of three distinct letters are possible if the three letters are chosen from the letters A, B, C, D, and E and A must be one of the letters selected?

A. 60
B. 10
C. 6
D. 4
E. 3[/quote
5c3= 10 we need to find out that A has to be included in the three group, and find how three group can be found out without the A.
4c3= 4 .
thus 10-4 equals 6.

FB2017 · Answer

Each group must have letter A and any two from the options BCDE.
Hence we should have 4C2 ways i.e. groups.
Option C.

Itisallinurhead · Answer

Thanks in advance for any response!!!

why is the below method not correct?
A _ _ , A has to be one of the letters. For the remaining 2 position it will be --> 4c1*3c1=12.

Since, the correct answer is 6, the possible groups are:
ABC, ABD, ABE, ACD, ACE, ADE.
Each group can again be arranged in 3! ways. So, What would the approach/solution be if the question asked for number of arrangements?

pushpitkc · Answer

Hi  Itisallinurhead

Here for the question being asked, in the 12 options possible when
you use 4c1*3c1 - AED and ADE are both possible(but since we are 
asked to find the total possible groups) it would be wrong!

If the question read - 
"total number of arrangements possible if A is one of the letters " 
One of the letters will be A.
The other two letter can be chosen as 4c2 = 6
There are 3!(6) ways of arranging them.

Total arrangments possible are 1*6*6 = 36

Hope this helps you!

ScottTargetTestPrep · Answer

First, we know this will be a combination problem, since the order of selection doesn’t matter.

Since A must be selected, we are actually choosing only 2 letters from the 4 letters: B,C,D,E. Thus, the selection can be made in 4C2 = (4 x 3)/2 = 6 ways.

Answer: C

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How many different groups of three distinct letters are possible if th

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