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
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: ^{14}C_{11 }= 364, but I'm unsure.
b) How many different teams are possible if the wicket keeper must be included?
I did ^{13}C_{11 }= 78, but I'm unsure.
c) How many different teams are possible if the team contains the wicket keeper, 6 batsmen and 4 bowlers?
Thanks in advance.
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