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There are 10 labelled balls (labelled 1,2,···10) and 10 labelled bins (labelled

ID: 2079534 • Letter: T

Question

There are 10 labelled balls (labelled 1,2,···10) and 10 labelled bins (labelled 1,2,···10). Even numbered balls are red, odd numbered balls are blue. Size of a subset refers to the number of items in the subset.
1. Find the number of ways of choosing 5 balls.
2. Find the number of ways I can put balls in bins, such that exactly two bins have one ball in them, and the remaining eight bins are empty.
3. Find the number of ways I can put balls in bins, such that each bin has one ball.
4. Find the number of ways I can put balls in bins, such that each bin has one ball, and even labelled bins have even labelled balls in them.
5. Find the number of ways I can choose 6 balls, such that the sum of their labels is even. 6. Find the number of ways I can choose 3 red balls and 2 blue balls.

Explanation / Answer

Answer 1

10C5 = 252

Answer 2

ways of choosing 2 ball 10C2 = 45

number of ways choosing 2 bins from 10 bins = 10C2 = 45

number of ways of putting one ball in one ball = 2

so here total no of ways is the answer is = 45*45*2 = 4050

Answer 3

10! = 3628800

Answer 4

5!*5! = 14400

Answer 5

so ways to six balls such that sun is even = no of ways to chose 6 balls/2 =10C6/2 =210/2 =105

Answer 6

number of ways choosing 3 red and 2 blue balls = 5C3 * 5C2 = 10*10 = 100