Mathematics I - Old Questions
Question Answer Details
b) What is the relation between permutation and combination of n objects taken r at a time? A committee of 5 is to be constituted from 6 boys and 5 girls. In how many ways can this be done so as to include at least a boy and a girl? (1+5)
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Official Answer
The relation between permutation and combination of n objects taken r at a time is derived as:
Now,
Total no. of students required to be chosen = 5
No. of boys = 6
No. of girls = 5
Total no. of ways to choose 5 students out of 11
students = 11C5 = 
The case where all committee has boys = 6C5
= 6
The case where all committee has girls = 5C5 =1
Therefore, The number of ways when at least1 boy and 1 girls are in
committee = 462-(6+1) = 455 ways