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Prove that (n!) (n + 2) = [n! + (n + 1)!...

Prove that `(n!) (n + 2) = [n! + (n + 1)!]`

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KUMAR PRAKASHAN-PERMUTATIONS AND COMBINATIONS-PRACTICE WORK
  1. Evaluate : (i) 2 xx 6! - 3 xx 5! (ii) (8!)/(4!) (iii) (20!)/(18!(2...

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  2. IF (n + 2)! = 2550 n! find n.

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  3. Prove that (n!) (n + 2) = [n! + (n + 1)!]

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  4. if 1/(7!)+1/(9!) =x/(10!) then find x.

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  5. Evaluate : ""((12!)-(10!)) / (9!)

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  6. How many words can be formed out of the letters of the word VOWEL. So...

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

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  8. How many words can be made form the letters of the word DAUGHTER assum...

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  9. How many three-digit numbers can be made using the digits 0, 1, 2, …, ...

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  10. From a committee of 10 persons, in how many ways can we choose a chair...

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  11. How many 3-digit even numbers that can be formed using the digit 2,4,6...

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  12. Find r : ""^(5) P(r) =42 ""^(6)P(r-1)

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  13. Prove that , ""^nPr = ""^((n-1))Pr + r. ""^(n-1)P((r-1))

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  14. If ""nPr=840 and ""^nCr=35, then r is equal to....

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  15. If ""^((n+2)) C8 :"" ^((n-2)) P4= 57 : 16 then find n.

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  16. If ""^nC10= ""^nC12 then find ""^23Cn.

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  17. In how many ways can a football team of 11 players be selected from 16...

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  18. A committee of 7 has to be formed from 9 boys and 4 girls. In how many...

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  19. A polygon has 65 diagonals, then find the number of its side.

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  20. What is the number of ways of choosing 4 cards from a pack of 52 play...

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