#### Ana

##### New member

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
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?