what is ⁿp_{r what is n factorial ?}

what is ⁿc_r plz explain their usage and meaning along with their formulae?

give some examples of questions with their usage

nPr is the number of Permutations of 'n' items taken 'r' at a time.

nCr is the number of Combinations of 'n' items taken 'r' at a time.

nPr = n! / (n-r)!

nCr = n! / [ (n-r)! * r! ]

n factorial is the product of n terms and the number of terms preceding it

suppose 'n' is  5 then 5! = 5*4*3*2*1 = 120

similarly n! = n*(n-1)*(n-2)*(n-3)*.......................*3*2*1

nCr is the number of combinations possible .

eg. there are 52 cards in a well shuffled deck. how many combinations are there in which a player can draw only 2 cards at a time ?

nPr is the number of permutations (possbilities).

HERE ARE SOME QUESTIONS YOU CAN PRACTICE.

1. There are four bus routes between A and B; and three bus routes
between B and C. A man can travel round-trip in number of ways by bus from A to C
via B. If he does not want to use a bus route more than once, in how many ways can
he make round trip?

2. How many numbers are there between 99 and 1000 having 7 in the units place?

Good Luck in your IIT-JEE preparation.

Please approve the answer.

dear nikhil

nPr means out of n population choose r elements and permute them. That is, choose r elements from n and give the total numbers of possibles orders there are.

nCr means out of n population choose r elements. That is, choose r elements from n and do not consider the different orders possible for the same choices of numbers.

So; nPr = nCr*r!