A, B, C, D, E, F, G, H, I K, K, L
A, C, D, E, F, G, H, I, J, K, L, B
A, D, E, F, G, H, I, J, K, L, B, C
A, E, F, G, H, I, J, K, L, B, C, D
A, F, G, H, I, J, K, L, B, C, D, E
A, G, H, I, J, K, L, B, C, D, E, F
A, H, I, J, K, L, B, C, D, E, F, G
A, I, J, K, L, B, C, D, E, F, G, H
A, J, K, L, B, C, D, E, F, G, H, I
A, K, L, B, C, D, E, F, G, H, I, J
A, L, B, C, D, E, F, G, H, I, J, K
That's 11 but then people in the middle could swap around too e.g.
A, B, C, D, E, F, G, H, I K, K, L
A, C, D, E, F, G, H, I, J, K, L, B
A, D, E, F, G, H, I, J, K, L, B, C
A, E, F, G, H, I, J, K, L, B, C, D
A, F, G, H, I, J, K, L, B, C, D, E
A, G, H, I, J, K, L, B, C, D, E, F
A, H, I, J, K, L, B, C, D, E, F, G
A, I, J, K, L, B, C, D, E, F, G, H
A, J, K, L, B, C, D, E, F, G, H, I
A, K, L, B, C, D, E, F, G, H, I, J
A, L, B, C, D, E, F, G, H, I, J, K
That's 11 but then people in the middle could swap around too e.g.
A, B, C, E, D, G, F, I, K, J, L, H
so there'd be more than 11, no?
the answer for A is 11! (factorial) = 39916800.
Quote:
Originally posted by RihannaRTT
QUESTION 4: In how many ways can 5 books be distributed among 10 people, if
(d) the 5 books are identical and each person can get any number of books
A - J
A gets 5, everyone else gets 0 (and so on) = 12
A gets 4, B gets 1, everyone else gets 0 = 12*11 = 132
A gets 3, B gets 2 (and so on) = see above = 132
A gets 3, B gets 1, C gets 1 = 12 * 11 * 10 = 1320
A gets 2, B gets 2, C gets 1 = see above = 1320
A gets 2, B, gets 1, C gets 1, D gets 1 = 12 * 11 * 10 *9 = 11880
A gets 1, B gets 1, C gets 1, D gets 1, E gets 1 = 12 * 11 * 10 * 9 * 8 = 95040
Oh, I love math/logic problems like this. too bad i was late
5b would be 6! times...something, I'm not sure. It's not just 6!
5c is 6! times 5! tho
YUP! these questions are so fun!
I see you're using the 'slotting in' way by using 6! times 5! for part (c), however since there are 6 couples, the options are much lesser since the couples have to sit with each other! so we just have to account for the arrangements of the 6 couples, instead of 6! x 5!
Haha since this thread is dead, i shall post the solutions.
Question 5: A group of 12 people consists of 6 married couples. The group stands in a circle.
(a) Find the number of possible arrangements Since they are standing in a circle, number of ways is given by (n-1)!
Therefore, number of possible arrangements = 11! = 39916800
(b) Find the number of different possible arrangements if men and women alternate Lets let the guys go i first. So, the number of ways for the guys to sit = 5!
Next we 'slot in' the girls. number of ways = 6!
Hence, total number of ways = 5! x 6! = 86400
(c) Find the number of different possible arrangements if each man stands next to his wife and the men and women alternate Since each man have to stand next to his wife, we have 6 couples. Number of ways to arrange six couples in a circle = 5!
Next we have to x2 as the men and women can swap places (within each couple).
nice try though!
so the numbers are 86 to 91
