There are 10 labelled balls (labelled 1, 2, ...10) and 10 labelled bins (labelle
ID: 3203656 • 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. Find the number of ways of choosing 5 balls. 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. Find the number of ways I can put balls in bins, such that each bin has one ball. Find the number of ways 1 can put balls in bins, such that each bin has one ball, and even labelled bins have even labelled balls in them. Find the number of ways I can choose 6 balls, such that the sum of their labels is even. Find the number of ways I can choose 3 red balls and 2 blue balls.Explanation / Answer
1)no of ways of chosing 5 balls = 10C5 = 252
2)no of ways of chosing 2 balls = 10C2 = 45
no of ways chosing 2 bins from 10 bins = 10C2 = 45
no of ways of putting one ball in one ball = 2
total no of ways = 45*45*2 = 4050
3)no of ways of putting on ball in one bin is same arranging 10 balls in a line = 10! = 3628800
4)no of ways putting even labelled balls in even bins and odd labelled balls in odd bins is same as arraging even labelled balls in a line and odd labelled balls in diffent line = 5!*5! = 14400
5)when we chose 6 balls we can sum as even or odd with equal probabilty becuase there are equal no of even and odd labels
so ways to six balls such that sun is even = no of ways to chose 6 balls/2 = 10C6/2 =210/2 =105
6)no of ways chosing 3 red and 2 blue balls = 5C3 *5C2 = 10*10 = 100
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