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Six children, three boys, and three girls sit in a row on a park bench 01 Jul 2020, 12:33
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D
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25% (medium)

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73% (01:49) correct 27% (02:06) wrong based on 115 sessions

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Six children, three boys, and three girls sit in a row on a park bench. How many arrangements of children are possible if no boy can sit on either end of the bench?

A. 46,656
B. 38,880
C. 1,256
D. 144
E. 38
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D
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Six children, three boys, and three girls sit in a row on a park bench 01 Jul 2020, 12:41
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Explanation:
Girls are fixed at both end seats., any girl can sit at the ends i.e. 3! = 6
So left 4 seats which will be shared by 3 boys & 1 girl.
4 can sit anywhere in middle seats = 4! = 24
Total possible arrangement is 6x24 = 144

IMO-D
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Six children, three boys, and three girls sit in a row on a park bench 01 Jul 2020, 13:09
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arrangement of G---BBBG---G

3 options for girl 1
3 options for boy 1
2 options for boy 2
1 option for boy 3
2 options for girl 2 and
1 option for girl 3
it sums up to 36.(3*3*2*2)
the girls at the end are set so we have 4 arrangement of the BBBG. so 144, but without calculations, A-C are huge for total arrangement with no restrictions (max 6!) and E is too low
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Six children, three boys, and three girls sit in a row on a park bench 01 Jul 2020, 16:27
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1 2 3 4 5 6

Let, above denote the number of benches.

Bench numbers 1 and 6 can only be occupied by a girl.

This can be done in: 3c2 * 2 ways

The other 4 children can be arranged in 4 places in 4! ways

=> Total = 3c2 * 2 * 4!
=> Total = 3 * 2 * 24
=> Total = 144

Answer: D

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Six children, three boys, and three girls sit in a row on a park bench 01 Jul 2020, 19:12
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IMO-D

Condition- boys will not sit either end of bench

No of ways boys can sit=3!
No of ways girls can sit=4*3!

Girls has total 4 place place to sit
_ B_B_B_
And they can sit as 3!

Total no of ways =6*6*4
=144

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Six children, three boys, and three girls sit in a row on a park bench 01 Jul 2020, 19:45
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IMO-D,
Since boys cannot sit at either end that is any 2 girls will occupy the ends of the bench.
Hence we need to select any 2 girls for the 2 ends which can be done by 3C2 and since these two girls can occupy any of the ends we need to arrange them also by multiplying by 2!.Thus 3C2*2! - arranges any girls for us for the two ends.
Now remaining 4 people can occupy the 4 left seats in 4! Ways.
Hence total => 3C2*2!*4!
=> 144

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Six children, three boys, and three girls sit in a row on a park bench 01 Jul 2020, 22:42
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total arrangements can be 6 ! ; 720 option a,b,c,d are out
now the possible ways ;
at two ends if we have girls fixed this can be done in 3c2 *2 ways
left with 4 positions which can be filled in 4! ways
total
3c2*2*4! ; 3*2*24 ; 144
OPTION D


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Six children, three boys, and three girls sit in a row on a park bench. How many arrangements of children are possible if no boy can sit on either end of the bench?

A. 46,656
B. 38,880
C. 1,256
D. 144
E. 38
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Six children, three boys, and three girls sit in a row on a park bench 01 Jul 2020, 23:29
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Bunuel
Six children, three boys, and three girls sit in a row on a park bench. How many arrangements of children are possible if no boy can sit on either end of the bench?

A. 46,656
B. 38,880
C. 1,256
D. 144
E. 38

No boy at any end

i.e. two girls to sit at ends and at one more chair which can be chosen in 4C1 ways (choosing 1 out of remaining 4 chairs for third girl)

Three girls at these three places (two ends and third chosen chair) can sit in 3! ways

remaining 3 boys can sit on remaining three chairs in 3! ways

Total outcomes = 4C1*3!*3! = 4*36 = 144

Answer: Option D
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Six children, three boys, and three girls sit in a row on a park bench 02 Jul 2020, 22:34
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choosing 2 girls out of 3 for both the end= 3C2
Number of ways to arrange 2 girls= 2
arranging rest of 4 children = 4!
hence 2* 3C2 * 4! = 144
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Six children, three boys, and three girls sit in a row on a park bench 04 Jul 2020, 09:32
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Bunuel
Six children, three boys, and three girls sit in a row on a park bench. How many arrangements of children are possible if no boy can sit on either end of the bench?

A. 46,656
B. 38,880
C. 1,256
D. 144
E. 38

Solution:

For the 2 seats at either end, there are 3 choices (since there are 3 girls) for one end and 2 choices (since 2 girls are left after one already sits at one end) for the other end. For the 4 seats in the middle, there are 4! = 24 ways to seat the remaining girl and the 3 boys. Therefore, there are a total of 3 x 2 x 24 = 144 ways to seat the 6 children with the 2 girls at either end of the bench.

Answer: D
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Six children, three boys, and three girls sit in a row on a park bench 01 May 2022, 06:06
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