how many ways can a group of three people order for ice cream from the menu of 12 different flavours each opting for a different flavour ?????
Answers
Given : three people order for ice cream from the menu of 12 different flavours each opting for a different flavour
To Find : Number of Ways
Solution:
3 People opting for a a different flavour
Hence 3 Flavour has to be selected out of 12 flavour
Number of ways of selecting 3 flavors = ¹²C₃
= 12!/9!. 3!
= 12 x 11 x 10 x 9 ! / 9! x 3 !
= 12 x 11 x 10 / 3!
= 12 x 11 x 10 / 3!
Now 3 Flavors in 3persons can be distributed in 3! ways
Hence Number of Ways three people order for ice cream from the menu of 12 different flavours each opting for a different flavour
= 3! * 12 x 11 x 10 / 3!
= 12 x 11 x 10
= 1320
in 1320 Ways three people can order for ice cream from the menu of 12 different flavours each opting for a different flavour
Other method:
1st person select in1 2 ways
2nd person select in 11 ways
3rd person select in 10 ways
12 x 11 x 10 = 1320
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