Abe, Bella, Cai, Dante, and Ellis each bring a present to a gift exchange. They each leave with someone else's gift. Abe left with Cai's gift and Dante left with Bella's. How many ways could the remaining gifts be distributed?
Answers
Given : Abe, Bella, Cai, Dante, and Ellis each bring a present to a gift exchange.
They each leave with someone else's gift.
Abe left with Cai's gift
Dante left with Bella's
To Find : How many ways could the remaining gifts be distributed?
Solution:
A left with C's Gift
D left with B's Gift
Person left Gift Left
B A
C D
E E
each leave with someone else's gift. and E can not get gift of E
hence E can get gift in 2 Ways
then B or C can get gift in 2 ways
and last one in 1 way
Hence 2 * 2 = 4 Ways
other way
3 person 3 gift = 3! = 6 ways
when E gets E then 2! = 2 Ways ( this case is not possible(
Hence 6 - 2= 4
remaining gifts can be distributed in 4 Ways
B - D , C -E , E - A
B - E , C -D , E - A
B - A , C -E , E - D
B - E , C -A , E - D
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