Home
Class 11
MATHS
(n!)/((n-r)!) = n(n-1)(n-2)...(n-(r-1))...

`(n!)/((n-r)!) = n(n-1)(n-2)...(n-(r-1))`

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise SECTION-B(Short anwer type question)|11 Videos

  • PERMUTATIONS AND COMBINATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise Section - C(Short answer type question)|21 Videos

  • PERMUTATIONS AND COMBINATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise SECTION-A(MCQ)|10 Videos

  • MATHEMATICAL REASONING

    CBSE COMPLEMENTARY MATERIAL|Exercise SECTION-B SHORT ANSWER TYPE QUESTIONS|5 Videos

  • PRACTICE PAPER DESIGN - I

    CBSE COMPLEMENTARY MATERIAL|Exercise SECTION -D|6 Videos

Similar Questions

Explore conceptually related problems

Prove that: (i) (n!)/(r!) = n(n-1) (n-2)......(r+1) (ii) (n-r+1). (n!)/((n-r+1)!) = (n!)/((n-r)!)

Prove that : (i) (n!)/(r!)=n(n-1)(n-2)...(r+1) (ii) (n-r+1)*(n!)/((n-r+1)!)=(n!)/((n-r)!) (iii) (n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!)=((n+1)!)/(r!(n-r+1)!)

If (1-x)^(-n)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(r)x^(r)+..., then a_(0)+a_(1)+a_(2)+...+a_(r) is equal to (n(n+1)(n+2)...(n+r))/(r!)((n+1)(n+2)...(n+r))/(r!)(n(n+1)(n+2)...(n+r-1))/(r!) none of these

Notation + theorem :- Let r and n be the positive integers such that 1<=r<=n. Then no.of all permutations of n distinct things taken r at a time is given by (n)(n-1)(n-2)....(n-(r-1))

(ii) (n!)/((n-r)!r!)+(n!)/((n-r+1)!(r-1)!)=((n+1)!)/(r!(n-r+1)!)

Prove that (n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!) =((n+1)!)/(r!(n-r+1)!)

Prove that (n-r+1)(n!)/((n-r+1)!)=(n!)/((n-r)!)

Prove that (n-r+1)(n!)/((n-r+1)!)=(n!)/((n-r)!)

Prove that ((n-1)!)/((n-r-1)!)+r.((n-1)!)/((n-r)!)=(n!)/((n-r)!)

Statement-1 : sum_(r=0)^(n) r^(2) ""^(n)C_(r) x^(r) = n (n-1) x^(2) (1 + x)^(n-2) + nx (1 +x)^(n-1) Statement-2: sum_(r=0)^(n) r^(2) ""^(n)C_(r) = n (n-1)2^(n-2)+ n2^(n-1) .