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A group consists of 4 girls and 7 boys. ...

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has
(i) no girls (ii) atleast one boy and one girl (iii) at least three girls

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The correct Answer is:
(i) =21 ways, (ii) =441 ways, (iii) =84+7=91 ways
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FULL MARKS-COMBINATORICS AND MATHEMATICAL INDUCTION-ADDITIONAL QUESTIONS
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  7. If ""^(nP(r)=""^(n)P(r+1) and ""^(n)C(r)=""^(n)C(r-1) find n and r.

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  8. A committee of 7 peoples has to be formed from 9 men and 4 women . In ...

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  11. If 1/(7!)+1/(9!)=x/(10!), find x.

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  12. If ""^(n)C(4),^(n)C(5)" and "^(n)C(6) are in A.P. then find n.

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  13. Prove by induction the inequality (1+x)^(n) ge 1 + nx. whenever x is p...

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  14. Prove that 3^(2n)-1 is divisible by 8.

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  15. Prove that x^n-y^n is divisible by x - y for all positive integers n.

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  16. Prove by mathematical induction that for every natural number n, 3^(2n...

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