permutation & Combination

2013-01-13 5:57 am

There are 12 different cans of cola.

a.How many ways to divide them into 4 groups,
such that there are 1 can,2 cans,4 cans and 5 cans in the respective groups?

b.How many ways to distribute the cans of cola to Kelvin,Howard,Dickson and
Peter, such that one of them gets 1 can,the other one gets 2 cans,
the third one gets 4 cans and the remaining one gets 5 cans?

c.How many ways to divide the cans of cola into 4 groups,
such that there are 3 cans in each groups?

d.How many ways to distribute the cans of cola to Mary,Gillian,Ada and Shirley,
such that each of them gets 3 cans of cola?

e.How many ways are there to arrange the cans of cola in a refrigerator
with 4 racks,such that there are 3 cans of cola on each rack?

Pls explain detail. THX A LOT

回答 (1)

50418129

2013-01-14 8:06 pm

✔ 最佳答案

(a)

choose 1 can from 12 to form group one, there are 12C1 methods.
choose 2 cans from remaining 11 to form group two, there are 11C2 methods.
choose 4 cans from remaining 9 to form group three, there are 9C4 methods.
choose 5 cans from remaining 5 to form group four, there are 5C5 methods.
so, required no. = 12C1 x 11C2 x 9C4 x 5C5

(b)

give four groups from (a) to four people in ramdoms,
required no. = 12C1 x 11C2 x 9C4 x 5C5 x 4P4

(c)

choose 3 cans from 12 to form group one, there are 12C3 methods.
choose 3 cans from remaining 9 to form group two, there are 9C3 methods.
choose 3 cans from remaining 6 to form group three, there are 6C3 methods.
choose 3 cans from remaining 3 to form group four, there are 3C3 methods.
with 4 groups are same size, thus, there will repeat 4P4 times
so, required no. = 12C3 x 9C3 x 6C3 x 3C3 / 4P4

(d)

same as (b)
required no. = (12C3 x 9C3 x 6C3 x 3C3 / 4P4) x 4P4

(e)

simply 12P12

參考: knowledge

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