Permutation Questions....HELP ME PLEASE?

Question

1. The letters of the word CAMBRIDGE are arranged such that the first five letters of the alphabet are in alphabetical order.  Find the number of different permutations. [ANS: 3024]

2. Two Families, each consisting of the father, the mother and a daughter, sit in a row.  In how many ways can they be seated such that each arrangement is SYMMETRICAL with respect to
(a) the 2 fathers, the 2 mothers and the 2 daughters. [ANS=6]

(b) the 2 men, the 2 women, and the 2 girls. [ANS=48]
How is part (b) different from part (a)???

THANKS.

Corretore · Answer

I do not understand the first part.  You have use combination.  We must use only permutation here.  I do not know how. Please Help me. Thanks..

? · Answer

1. CAM BRI DGE has 9 letters. There are 9C5 = 126 ways to pick the first 5 letters, but for each of those there is only one arrangement in alphabetical order. The remaining 4 letters can be in any of 4! = 24 orders. The answer is 126x24 = 3024

2. You can seat one family in 3! = 6 ways. Then the other family's seating is determined. So that's way the answer is 6.

3. You can arrange the 3 groups in 3! = 6 ways:
MWG
MGW
WMG
WGM
GMW
GWM

And for each of those, you have 2 ways to arrange the men, 2 ways to arrange the women, and 2 ways to arrange the girls. 2x2x2 = 8
6 x 8 = 48 is the answer.

How is it different? The requirements are different. Not sure how else to describe it.

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Permutation Questions....HELP ME PLEASE?

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