in 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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Step-by-step explanation:
Given in 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?
- So the menu consists of 12 flavours. So three flavours need to be selected out of 12 flavours.
- So number of ways for selecting three flavours will be 12 P3
- So we have nPr = n! / (n – r)!
- 12P3 = 12! / (12 – 3)!
- = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
- = 12 x 11 x 10
- = 120 x 11
- = 1320
- So number of ways to order for ice cream from 12 different flavours will be 1320
Reference link will be
https://brainly.in/question/10849988