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Prove that 3lerlen ""^(n-3)C(r)+3""^(n...

Prove that `3lerlen`
`""^(n-3)C_(r)+3""^(n-3)C_(r-1)+3""^(n-3)C_(r-2)+""^(n-3)C_(r-3)=""^(n)C_(r)`

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The correct Answer is:
`=""^(n)C_(r)`
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AAKASH SERIES-PERMUTATIONS & COMBINATIONS-PRACTICE EXERCISE
  1. Prove that 3lerlen ""^(n-3)C(r)+3""^(n-3)C(r-1)+3""^(n-3)C(r-2)+""^(...

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  2. IF ""^(10)p r = 5040 then r=

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  3. If ""^(n)P(5)=""^(n)P(6) then n is

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  4. If ""^((n+1))P(5): ""^(n)P(5)=3:2, find n

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  5. If ""^(n)P(4):""^(n)P(3)=2:1 then is

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  6. IF ""^((2n-1))P(n-1) : ""^((2n-1))Pn = 3:5 then n=

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  7. There are 12 balls numbered from 1 to 12. The number of ways in which ...

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  8. There are 50 stations on a railway line. The number of different kinds...

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  9. The number of arrangements that can be formed by taking all the ...

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  10. The letters of the word “FLOWER” are taken four at a time and arranged...

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  11. The number of arrangements that can be formed by taking all the letter...

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  12. The different words beging and ending with a vowel that can ma...

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  13. The number of ways in which the letters of the word 'FRACTION' be arra...

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  14. The number of ways in which the letters of the word 'FRACTION' be arra...

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  15. The number of ways in which the letters of the word 'FRACTION' be arra...

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  16. The number of arrangements that can be made by using all the le...

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  17. How many ways are there to arrange the letters in the word G...

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  18. Find the number of ways of arranging the letters of the word TRIANGLE ...

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  19. The letters of the word 'MADHURI' are arranged in all possible ways. T...

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  20. The number of four digited numbers that can be formed using the digits...

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  21. The number of 5 digited numbers using 0, 1, 2,3, 4 no digit being repe...

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