A Manager needs 4 different teams (named P, Q, R, S) for doing project

Official Solution:

Here 8 persons to be divided into 4 groups of 2 people each.

So answer = 8!/(2!2!2!2!) = 2520 = Answer E


See this for the complete concept : https://gmatclub.com/forum/dividing-objects-into-groups-combinations-266092.html

8 people divided into 4 teams of 2 each can be done in
\(\frac{8!}{2!*2!*2!*2!}\) = 2520

Option E

If we compute permutations of elements, the number would be: 8!

In this case, the permutation
A B C D E F G H
would represent:
{A, B}, {C, D}, {E, F}, {G, H}

But that would be the same as:
{B, A}, {C, D}, {E, F}, {G, H}

That is, for any of the 4 groups, the order doesn’t matter… and you have 2 possible ways for every “pair”.
So, you have to divide by (2*2*2*2)

So, that would be:
8! / (2*2*2*2)

But that would be if the order of the 4 groups matters… if
{A, B}, {C, D}, {E, F}, {G, H}
is different from
{C, D}, {A, B}, {E, F}, {G, H}
Which is basically the same as the former but he {A, B} is in the “second group” instead of the “first group”.

If the order of the 4 groups doesn’t matter, then we have to divide by the number of ways you can order the 4 groups, that is, the permutations of 4 ‘elements’, which is: 4!

4*7*3*5*2*3 / 4! = 7*5*3 = 105

Answer is B

Posted from my mobile device

ANS: B (105)

8C2 * 6C2 * 4C2 * 2C2/ 4!
= 105

Hope it is right....

since 8 people are to be divided into 4 teams of 2 each
8!/(2!)^4 = 2520

ANSWER IS E



8C2 x 6C2 x 4C2

= 2520

IMO E

Total No. of persons for selection = 8
Teams to be formed = 4
No. of people in each team = 2

Now, total ways of making team P = Select 2 out of 8 people = 8C2 = 28
Similarly. total ways of making team Q = Select 2 out of remaining 6 people = 6C2 = 15
For R = Select 2 out of remaining 4 people = 4C2 = 6
For S = Select 2 out of remaining 6 people = 2C2 = 1

Therefore, Total Possible ways to make the teams P,Q,R,S = 28x15x6x1= 2520

E. 2520

Projects : --A--B--C--D--
Teams : --P--Q--R--S--

This is just the number of different arrangements in which we can make 4 teams of 2 people each from a group of 8 people

That is 8C2*6C2*4C2*2C2 = 28*15*6*1 = 2520

Answer is (E)

Given: A Manager needs 4 different teams (named P, Q, R, S) for doing projects A, B, C, D respectively.
Asked: In how many different ways can a group of 8 people be divided into 4 teams of 2 people each for carrying out the Projects?
A. 90
B. 105
c. 168
D. 420
E. 2520

Let 8 persons be designated as:

P1 P2 Q1 Q2 R1 R2 S1 S2

Total number of different ways can a group of 8 people be divided into 4 teams of 2 people each for carrying out the Projects = 8!/2^4 = 2520

IMO E

A Manager needs 4 different teams (named P, Q, R, S) for doing projects A, B, C, D respectively. In how many different ways can a group of 8 people be divided into 4 teams of 2 people each for carrying out the Projects?
A. 90
B. 105
c. 168
D. 420
E. 2520

total possible ways
8c2*6c2*4c2*2c2/ 4! ;
solve we get 105
OPTION B

Out of 8 people select 2 people to form first team
then out of remaining (8-2=)6 people choose 2 people ..then 2 people from 4 and at last 2 from 2.
since there are 4 teams with identical team size=2 , we divide by 4!
{8C2 * 6C2 * 4C2 * 2C2 }/ 4!=105
P,Q,R and s=so multiply by 4!
=2520>> option E

Hello

E is the right answer

Totally 4 different teams have to be formed.So we cannot have any repetition.

1st : 8 C 2 *
2nd : 6 C 2 *
3rd : 4 C 2 *
4th : 2 C 2

Equals 2520.

Best

Posted from my mobile device

We have 8 people to fit into 8 slots(4 groups * 2 members each) and, the number of ways that can happen is 8!. But, there are only 4 unique slots and rest is a replica of the first four. Something like this P, Q, R, S, P, Q, R, S. Now you can re-interpret what the question is asking, in how many ways can you arrange the letters of the word PPQQRRSS (remember MISSISSIPPI)? And the answer is, 8!/(2!2!2!2!)= 2520.

I figured out that there is another way to solve this with logic.

Step 1- Pick two members of group P from 8 people. Number of ways we can do that is 8C2= 28.
Step 2- Pick two members of the team Q from remaining 6 people. Number of ways we can do that is 6C2= 15.
Step 3- Pick members of team R from remaining 4 people. # Ways to do that is 4C2=6.
Step 4- Last two remaining form the group S.

Hence, the number of ways we can make 4 teams of 2 people each from 8 members = 28*15*6*1= 2520.

Hope it helps

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