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Gordon buys 5 dolls for his 5 nieces. The gifts include two identical S beach dolls, one E, one G, one T doll. If the

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by BTGmoderatorDC » Mon Feb 03, 2020 8:32 pm
Gordon buys 5 dolls for his 5 nieces. The gifts include two identical S beach dolls, one E, one G, one T doll. If the youngest niece doesn't want the G doll, in how many different ways can he give the gifts?

A. 12
B. 24
C. 36
D. 48
E. 60


OA D

Source: Manhattan Prep
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Re: Gordon buys 5 dolls for his 5 nieces. The gifts include two identical S beach dolls, one E, one G, one T doll. If th

by Jay@ManhattanReview » Mon Feb 03, 2020 9:37 pm
BTGmoderatorDC wrote: ↑
Mon Feb 03, 2020 8:32 pm
 Gordon buys 5 dolls for his 5 nieces. The gifts include two identical S beach dolls, one E, one G, one T doll. If the youngest niece doesn't want the G doll, in how many different ways can he give the gifts?

A. 12
B. 24
C. 36
D. 48
E. 60

OA D

Source: Manhattan Prep
The distribution of 5 dolls are

• S type -- 2;
• E type -- 1;
• G type -- 1;
• T type -- 1;

Number of ways, the 5 dolls can be distributed among 5 girls = 5!/2! = 60; we divided 5! by 2! since there are two S type identical dolls.

However, in the 60 ways, there are ways in which the youngest niece would have G type doll; we must exclude those ways.

Say, the youngest niece got G type doll.

Thus, the number of ways, the remaining 4 dolls can be distributed among the remaining 4 girls = 4!/2! = 12;

Required ways = 60 – 12 = 48

The correct answer: D

Hope this helps!

-Jay
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