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The combinatorial coefficients ""^(n – 1...

The combinatorial coefficients `""^(n – 1)C_(p)` denotes

A

The number of ways in which 'n' things of which 'p' are alike and rest different can be arranged in a circle

B

The number of ways in which 'p' different things can be selected out of 'n' different thing if a particular thing is always excluded

C

Number of ways in which n alike balls can be distributed in 'p' different boxes so that no box remains empty and each box can hold any number of balls.

D

The number of ways in which (n – 2) white balls and p black balls can be arranged in a line if black balls are separated, balls are all alike except for the colour.

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The correct Answer is:
B, D
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The combinatorial coefficient C(n, r) is equal to

Statement-1 : The sum of the series ^nC_0. ^mC_r+^nC_1.^mC_(r-1)+^nC_2.^mC_(r-2)+......+^nC_r.^mC_0 is equal to ^(n+m)C_r, where C's and C's denotes the combinatorial coefficients in the expansion of (1 + x)^n and (1 + x)^m respectively, Statement-2: Number of ways in which r children can be selected out of (n + m) children consisting of n boys and m girls if each selection may consist of any number of boys and girls is equal to ^(n+m)C_r

If ""(n)C_(0), ""(n)C_(1), ""(n)C_(2), ...., ""(n)C_(n), denote the binomial coefficients in the expansion of (1 + x)^(n) and p + q =1 sum_(r=0)^(n) r^(2 " "^n)C_(r) p^(r) q^(n-r) = .

If ""^(n)C_(0), ""^(n)C_(1),..., ""^(n)C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) and p + q = 1 , then sum_(r=0)^(n) ""r.^(n)C_(r) p^(r) q^(n-r) =

If n be a positive integer and P_(n) denotes the product of the binomial coefficients in the expansion of (1+x)^(n), prove that (P_(n+1))/(P_(n))=((n+1)^(n))/(n!)

If C_(0), C_(1), C_(2),…, C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then sum_(r=0)^(n)sum_(s=0)^(n)(C_(r) +C_(s))

If C_(0), C_(1), C_(2), …, C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then sum_(r=0)^(n)sum_(s=0)^(n)C_(r)C_(s) =

MOTION-THEORY AND EXERCISE BOOK-EXERCISE - 2 (LEVEL -II)
  1. The combinatorial coefficient C(n, r) is equal to

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  2. The continued product 2.6.10.4…..(n times) in equal to

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  3. The maximum number of permutation of 2n letters in which there are onl...

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  4. If P(n, n) denotes the number of permutations of n different things ta...

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  5. Consider the letters of the word 'MATHEMATICS' Possible number of wor...

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  6. Consider the letters of the word 'MATHEMATICS Possible number of words...

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  7. Consider the letters of the word 'MATHEMATICS Possible number of words...

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  8. Column–I (A) In a plane a set of 8 parallel lines intersect a set of...

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  9. Number of ways in which three numbers in AP can be selected from 1,2,3...

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  10. The combinatorial coefficients ""^(n – 1)C(p) denotes

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  11. 16 players P1,P2,P3,.. P16 take part in a tennis tounament. Lower suff...

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  12. 16 players P(1),P(2),P(3),….P(16) take part in a tennis tournament. Lo...

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  13. 16 players P(1),P(2),P(3),….P(16) take part in a tennis tournament. Lo...

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  14. Which of the following statements are correct ?

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  15. Identify the correct statement(s)

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  16. The number of ways in which five different books to be distributed amo...

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  17. Column–I (A) Four different movies are running in a town. Ten stude...

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  18. There are 10 questions, each question is either True or False. Number ...

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