Home
Class 11
MATHS
Prove the following: n(Pn)​= n(P(n−1))...

Prove the following: `n_(P_n)​`= `n_(P_(n−1))`

Text Solution

AI Generated Solution

To prove the equation \( n_{P_n} = n_{P_{n-1}} \), we will use the definition of permutations and simplify both sides step by step. ### Step 1: Understand the Definition of Permutations The notation \( n_{P_r} \) represents the number of permutations of \( n \) items taken \( r \) at a time, which is given by the formula: \[ n_{P_r} = \frac{n!}{(n-r)!} \] ...
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    RD SHARMA|Exercise Solved Examples And Exercises|81 Videos

  • PROBABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|280 Videos

Similar Questions

Explore conceptually related problems

Prove the following: P(n,n)=2P(n,n-2)

Prove the following: P(n,r)=ndot P(n-1,r-1)

Prove the following: P(n,r)=P(n-1,r)+rdot P(n-1,r-1)

Prove that: (i) ""^(n)P_(n)=""^(n)P_(n-1) " (ii) "^(n)P_(r)=n* ""^(n-1)P_(r-1) " (iii) "^(n-1)P_(r)+r* ""^(n-1)P_(r-1)=""^(n)P_(r)

Prove that quad if r<=s<=n then ^(^^)n_(P_(s)) is divisible by ^(^^)n_(P_(r))

In any G.P. , prove that a_(n-p) xxa_(n+p) = (a_(n))^(2) .

It is tossed n xx.Let P_(n) denote the probability that no two (or more) consecutive heads occur.Prove that P_(1)=1,P_(2)=1-p^(2) and P_(n)=(1-P)P_(n-1)+p(1-P)P_(n) for all n<=3.