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Find the number of 4-digit numbers that ...

Find the number of 4-digit numbers that can be formed using the digits 1,2,3,4,5 if no digit is repeated. How many of these will be even ?

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FULL MARKS-COMBINATORICS AND MATHEMATICAL INDUCTION-ADDITIONAL QUESTIONS
  1. We wish to select 6 person from 8 but , if the person A is choosen , t...

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  2. How many 3-digit numbers can be made using digit 1,2,3,4,6,7 if no dig...

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  3. Find the number of 4-digit numbers that can be formed using the digits...

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  4. Iff ""^(5)P(r)=""^(6)P(r-1) find r.

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  5. How many words, with or without meaning , can be made from the letters...

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  6. A group consists of 4 girls and 7 boys. In how many ways can a team of...

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  7. A committee of 6 is to be choosen from 10 men and 7 women so as to con...

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  8. Using the digits 1,2,3,4,5,6,7 a number of 4 different digits is forme...

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  9. If ""^(22)P(r+1):^(20)P(r+2)=11:52, find r.

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  10. If ""^(nP(r)=""^(n)P(r+1) and ""^(n)C(r)=""^(n)C(r-1) find n and r.

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

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  12. In .^(2n)C(3) :.^(n)C(3) = 11 : 1 then n is

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  13. Find the number of ways of selecting 9 balls from 6 red balls, 5 white...

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

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

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

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

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

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

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  20. Use the principle of mathematical induction to prove that for every na...

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