Please help me with these problems

Ana

New member
Joined
May 10, 2012
Messages
1
I really have no idea how to do these, please help:

1) Three women and seven men must form a queue. Find:

a) The number of different queues possible. (My answer: 10!)

b) The number of queues in which the women are all gattered in a single block. (My answer: 48 x 7! or 241,920)

c) The number of queues in which two women never stay together.

d) The number of queues in which each man can only stay beside, at maximum, one woman.

If you would explain too, I really need to learn this!
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
7,961
1) Three women and seven men must form a queue. Find:

a) The number of different queues possible. (My answer: 10!) CORRECT.

b) The number of queues in which the women are all gattered in a single block. (My answer: 48 x 7! or 241,920)

c) The number of queues in which two women never stay together.
b) Think of the women as one block. Now we arrange eight blocks. But the women can be arranged in \(\displaystyle 3!\) ways.

c) The men create eight spaces for the women: __m__m__m__m__m__m__m__.
Choose three spaces, \(\displaystyle \binom{8}{3}(3!)(7!)\) WHY?
 
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