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# In how many ways can 5 boys and 4 girls be arranged in a line so that

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Math Expert
Joined: 02 Sep 2009
Posts: 64314
In how many ways can 5 boys and 4 girls be arranged in a line so that  [#permalink]

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16 Apr 2019, 20:47
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15% (low)

Question Stats:

77% (01:41) correct 23% (02:17) wrong based on 77 sessions

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In how many ways can 5 boys and 4 girls be arranged in a line so that there will be a boy at the beginning and at the end?

(A) 3!/5! * 7!

(B) 5!/6! * 7!

(C) 5!/3! * 7!

(D) 3!/5! * 7!

(E) 5!/7! * 7!

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Re: In how many ways can 5 boys and 4 girls be arranged in a line so that  [#permalink]

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16 Apr 2019, 21:13
5
B _ _ _ _ _ _ _ B

The two boys can be selected in $$^5C_2$$ ways and can be arranged in 2! ways. The remaining 7 people can be selected in 1 way and can be arranged in 7! ways.

$$\frac{5!}{2!*3!}*2! * 7!$$

$$\frac{5!}{3!}*7!$$

OPTION: C
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Re: In how many ways can 5 boys and 4 girls be arranged in a line so that  [#permalink]

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16 Apr 2019, 22:47
Bunuel wrote:
In how many ways can 5 boys and 4 girls be arranged in a line so that there will be a boy at the beginning and at the end?

(A) 3!/5! * 7!

(B) 5!/6! * 7!

(C) 5!/3! * 7!

(D) 3!/5! * 7!

(E) 5!/7! * 7!

total arragements of boys
5c2 *2 ways and total places left after 2 boys occupy first and last position 7
so 5c2*2*7!
IMO C 5!/3! * 7!
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Re: In how many ways can 5 boys and 4 girls be arranged in a line so that  [#permalink]

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22 Apr 2019, 02:45
Bunuel wrote:
In how many ways can 5 boys and 4 girls be arranged in a line so that there will be a boy at the beginning and at the end?

(A) 3!/5! * 7!

(B) 5!/6! * 7!

(C) 5!/3! * 7!

(D) 3!/5! * 7!

(E) 5!/7! * 7!

The way the answers are given , thought that 7! is in the denominator.

B-------B
5*7*6*5*4*3*2*1*4
That's option C
$$\frac{5!}{3!}*7!$$
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Re: In how many ways can 5 boys and 4 girls be arranged in a line so that  [#permalink]

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10 Aug 2019, 02:03
Slight confusion.

When we say 7!, aren't we considering all 7 elements to be distinct ? Where as there are 3 Boys and 4 Girls. Why are we considering each boy to be different and each girl to be different ?

Will appreciate a response.
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Re: In how many ways can 5 boys and 4 girls be arranged in a line so that  [#permalink]

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10 Aug 2019, 02:11
Slight confusion.

When we say 7!, aren't we considering all 7 elements to be distinct ? Where as there are 3 Boys and 4 Girls. Why are we considering each boy to be different and each girl to be different ?

Will appreciate a response.

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Aren't all people different?
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Re: In how many ways can 5 boys and 4 girls be arranged in a line so that  [#permalink]

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10 Aug 2019, 04:10
Bunuel wrote:
Slight confusion.

When we say 7!, aren't we considering all 7 elements to be distinct ? Where as there are 3 Boys and 4 Girls. Why are we considering each boy to be different and each girl to be different ?

Will appreciate a response.

______________________
Aren't all people different?

How can I determine if B1B2b3B4 are to be taken as 4 distinct objects or same ? I am comparing this scenario to ABCCADA. The letters are repeating, much like the boys and girls in this question. Why didn't we divide the Boys and Girls 7! by 4! X 3!.

Thanks againm

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Re: In how many ways can 5 boys and 4 girls be arranged in a line so that  [#permalink]

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10 Aug 2019, 04:19
1
Bunuel wrote:
In how many ways can 5 boys and 4 girls be arranged in a line so that there will be a boy at the beginning and at the end?

(A) 3!/5! * 7!

(B) 5!/6! * 7!

(C) 5!/3! * 7!

(D) 3!/5! * 7!

(E) 5!/7! * 7!

Number of ways of arranging 2 boys at the ends = 5p2 = 5!/3!

The remaining 7 people can be arranged in 7! Ways

So, total = 5!/3!*7!

Option C

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Re: In how many ways can 5 boys and 4 girls be arranged in a line so that   [#permalink] 10 Aug 2019, 04:19