pemdas wrote:In how many ways can 21 post mails be distributed among seven couriers such that each courier receives an equal amount of post mails?
A 21^7
B (7!)^7
C 21!/(3!)^7
D 21!/7!
E 7^21
made up
Because we are ASSIGNING combinations of 3 to each courier, the ORDER of the groupings matters.
Assigning
ABC to courier 1 and DEF to courier 2 is not the same as assigning
DEF to courier 1 and ABC to courier 2.
Step 1: Count how many combinations of 3 can be assigned to each courier.
Step 2: Multiply the results in order to count the number of ways in which these combinations of 3 can be ORDERED among all 7 couriers.
Combinations of 3 that could be assigned to the first courier:
(21*20*19)/3!.
Combinations of 3 that could be assigned to the second courier:
(18*17*16)/3!.
Combinations of 3 that could be assigned to the third courier:
(15*14*13)/3!.
And so on.
When we multiply these results:
The numerator will be 21!: (21*20*19)*(18*17*16)*(15*14*13)....
Since each of the 7 groupings is divided by 3!, the denominator will be (3!)(3!)(3!)(3!)(3!)(3!)(3!) = (3!)�.
Thus, the correct answer here is
C: 21!/(3!)�.
This expression represents the number of ways to ARRANGE 7 combinations of 3.
In other words, the number of ways we can ASSIGN 3 letters to each of the 7 couriers.
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