A team of 4 boys and 5 girls is to be made from a team of 7 boys and 8

Question

A team of 4 boys and 5 girls is to be made from a team of 7 boys and 8 girls. Sam, who is one of the boys,
is selected only if his sister, Eloise, who is one of the girls is also selected. In all, how many different teams
are possible?

A. 315
B. 630
C. 1015
D. 1540
E. 2450

Source: Experts Global

A. 315
B. 630
C. 1015
D. 1540
E. 2450

Source: Experts Global

ScottTargetTestPrep · Accepted Answer

We can see that the only way a team is NOT possible is if Sam makes the team, but his sister doesn’t. Therefore,
 
The number of ways a team can be selected = the total number of ways a team can be selected without any restrictions - the number of ways a team is selected with Sam in it but not his sister

The total number of ways a team can be selected without any restrictions is the number of ways to select 4 boys from 7 and 5 girls from 8, which is:

7C4 x 8C5 = (7 x 6 x 5 x 4)/(4 x 3 x 2 x 1) x (8 x 7 x 6 x 5 x 4)/(5 x 4 x 3 x 2 x 1) = 35 x 56 = 1960

The number of ways a team is selected with Sam in it but not his sister is:

1C1 x 6C3 x 1C0 x 7C5 = (6 x 5 x 4)/(3 x 2 x 1) x (7 x 6 x 5 x 4 x 3)/(5 x 4 x 3 x 2 x 1) = 20 x 21 = 420

Thus, the number of ways a team can be selected is 1960 - 420 = 1540.

Answer: D

saraheja · Answer

Two cases :

1) When boy is selected so for sure girl would have been selected , so no. of ways would be 6C3 * 7C4 = 700

2) When that boy is not selected - 6C4 * 8C5 = 840

total 1540

GMATinsight · Answer

Favourable cases = Total ways of selecting team - teams with the brother without sister = 7C4*8C5 - 6C3*7C5 = 35*56 - 20*21 = 1540

Hero8888 · Answer

I did the same calculation. How did you get 840 from 6C4 * 8C5 ? I constantly get (15*42) = 630.

Hero8888 · Answer

Does that mean that there is a number of outcomes included in 1540, in which the sister can go without brother? Because I see that you deducted only the case when brother goes without sister. Thanks

RidhimaGmat · Answer

8C5 = 8!/3! 5! = 56, 
6C4 * 8C5 = 15 * 56 = 840

Hero8888 · Answer

Omg, my arithmetic sucks, thanks.

smritisingh8 · Answer

Both selected - 6c3 + 7c4 Sam not selected - 6c4 + 8c5 We add the above two to get the answer. Remember spending a lot of time on this one while attempting Experts Global mock and getting it incorrect

Sent from my SM-T285 using GMAT Club Forum mobile app

smritisingh8 · Answer

Yes, my friend. That is the catch in the question.

Reading carefully. The brother comes only if sister does but the sister can come alone.

It's so important to understand the nuanced meaning in such questions.

Good stuff.

Sent from my SM-T285 using  GMAT Club Forum mobile app

Pritishd · Answer

1. Total boys and girls are  7  and  8  respectively. And  4  boys and  5  girls are to be selected for the team

2. There will be  3  cases. Let's assume variables for Eloise getting selected as  E  and not getting selecting as  NE . Similarly,  S  and  NS  for Sam

CASE - I:    E  &  S   = (1 * 7C4) * (1 * 6C3) = 35 * 20 = 700

CASE - II:    E  &  NS   = (1 * 7C4) * (6C4) = 35 * 15 = 525

CASE - III:    NE  &  NS   = (7C5) * (6C4) = 21 * 15 = 315

3. Summing up the three cases  = 700 + 525 + 315 = 1,540

Ans.  D

Oppenheimer1945 · Answer

1) Case 1: E selected: S may or may not be selected: 7C4.7C4
2) Case 2: E not selected, S not selected: 7C5.6C4

35.35+21.15=5.7(35+9)=5.7.44

check option with last digit 0 and div by 11 : 1540 D)

Gemmie · Answer

1. Teams where Sam and Eloise are both selected

Now, calculate the number of teams where Sam is selected, and therefore, Eloise must also be selected.

If Sam is selected, we need to choose 3 more boys from the remaining 6:  6C3 = \frac{6!}{3! * 3!} = 20

Since Eloise is selected, we need to choose 4 more girls from the remaining 7:  7C4 = \frac{7!}{4! * 3!} = 35

Total number of teams where both Sam and Eloise are selected: 20 * 35 = 700

2. Teams where Sam is not selected

If Sam is not selected, Eloise may or may not be selected. Therefore, we can calculate the number of teams where Sam is not selected.

If Sam is not selected, we need to choose all 4 boys from the remaining 6: 6C4 = 15

The number of ways to choose 5 girls from 8 remains: 8C5 = 56

Total number of teams where Sam is not selected: 15 × 56 = 840

==> Total number of valid teams:  700 + 840 = 1540

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A team of 4 boys and 5 girls is to be made from a team of 7 boys and 8

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