In how many ways can 11 # signs and 8 * signs be arranged in a row so

Question

In how many ways can 11 # signs and 8 * signs be arranged in a row so that no two * signs come together?

A. 108
B. 126
C. 252
D. 495
E. 990

chetan2u · Answer

Let us put # with a gap between two consecutive signs. 
_,#,_,#,_,#,_,#,_,#,_,#,_,#,_,#,_,#,_,#,_,#,_
So 11 of # will give 12 spaces for placing 8 of *.

We can pick 8 spaces out of 12 in 12C8 ways -=> \frac{12*11*10*9}{4*3*2*1}=495

D

KarishmaB · Answer

It is just like the boys and girls questions in which no two girls can sit together. The point to first make the boys sit and let the girls occupy spaces between them. Hence the difference is that the signs are not distinct.

So arrange all 11 # in one row in 1 way. Then we have 12 spots for the *s. Select 8 of the 12 spots and put all 8 * in them. Again no arrangement is required because all * are identical.

12C8 = 12*11*10*9/4*3*2*1 = 495

Answer (D)

hr1212 · Answer

One other approach here could also be to place all 8 * signs and 7 # signs in the middle. The problem now requires us to feel in 9 gap areas around 8 * signs with remaining 4 # signs. Kind of a variant of beggars problem where you have to divide 4 things among 9 variables.

r1 + r2 + r3 + ... + r9 = 4

Solution for such equations is n+r-1Cr-1 = (9+4-1)C(9-1) = 12C8 = 495

IMO: D

pk14y · Answer

For this question, I kind of grouped the "*#" together and solved it like MISSISSIPPI problem.

I got 11!/8!3! from there and got 165, and then I multiplied it by 2 because the grouping could also be "#*" and got 330. Now of course its not there, but I still answered D because it was the closest value with 165 * 3. However, I'm not sure what exactly I'm doing wrong, or what case I'm forgetting. Can somebody add some input?

Bunuel · Answer

's and #'s are identical, so arranging those does not make sense. Check the methods described above.

bumpbot · Answer

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In how many ways can 11 # signs and 8 * signs be arranged in a row so

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In how many ways can 11 # signs and 8 * signs be arranged in a row so

Prep Toolkit

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