1. ## Permutations and Combinations

Q1: The number of ways 8 people can be arranged in a straight line if two people insist on being separated is:
A) 15,120
B) 3,600
C) 30,240
D) 7,200
E) 5,400

No matter what I try I can't obtain any of these possible answers. I'm thinking it's something to do with the wording of the question, but I'm not sure what exactly.

Q2: A cricket team takes 11 players to a game and there are 14 players from which to choose; 1 wicket keeper, 7 batsmen and 6 bowlers.
a) How many different teams are possible if there are no restrictions?

I did: 14C11 = 364, but I'm unsure.

b) How many different teams are possible if the wicket keeper must be included?
I did 13C11 = 78, but I'm unsure.

c) How many different teams are possible if the team contains the wicket keeper, 6 batsmen and 4 bowlers?

2. ## Re: Permutations and Combinations

Hello, Fratricide!

Q1: the number of ways 8 people can be arranged in a straight line
. . . if two people insist on being separated is:

. . (A) 15,120 . . (B) 3,600 . . (C) 30,240 . . (D) 7,200 . . (E) 5,400

$\text{The eight people are: }\:\{A,B,C,D,E,F,G,H\}$

$\text{Let }A\text{ and }B\text{ be the two unfriendly people.}$

$\text{With no restrictions, there are }\,8! = 40,\!320\text{ arrangements.}$

$\text{Now consider the arrangements in which }A\text{ and }B\:are\text{ adjacent.}$

$\text{Duct-tape }A\text{ and }B\text{ together.}$
$\text{Then we have 7 "people" to arrange: }\,\left\{\boxed{AB}, C, D, E, F, G, H\right\}$
$\text{There are: }\,7!\text{ arrangements.}$

$\text{But }A\text{ and }B\text{ could be taped like this: }\,\boxed{BA}.$

$\text{Hence, there are: }\,2\cdot7! \,=\,10,\!080\text{ ways in which }A\text{ and }B\text{ are adjacent.}$

$\text{Therefore, the answer is: }\:40,\!320 - 10,\!080 \:=\:30,\!240\:\text{ . . . answer (C)}$

3. ## Re: Permutations and Combinations

Hello
I think you are right in Q2(a)

(b) 13C10( because the wicket keeper must be include)
(c) 7C6x6C4

4. ## Re: Permutations and Combinations

Originally Posted by Trefoil2727
Hello
I think you are right in Q2(a)

(b) 13C10( because the wicket keeper must be include)
(c) 7C6x6C4
Could you please elaborate on (c) to clarify my understanding?

5. ## Re: Permutations and Combinations

Originally Posted by Fratricide
Could you please elaborate on (c) to clarify my understanding?
well I really not good on explanation, because my English is sucked, but I'll try..
you have to choose 11 players, and there is only 1 wicket keeper, which you have to count in. So there left only 13 people to choose, as the question ask to have 6 batsmen( from 7) and 4 bowlers( from 6). Therefore, 7C6x6C4

6. ## Re: Permutations and Combinations

Originally Posted by Trefoil2727
well I really not good on explanation, because my English is sucked, but I'll try..
you have to choose 11 players, and there is only 1 wicket keeper, which you have to count in. So there left only 13 people to choose, as the question ask to have 6 batsmen( from 7) and 4 bowlers( from 6). Therefore, 7C6x6C4
Perfect, thanks.