A P Prabhakaran Solutions for Chapter: Permutations and Combinations, Exercise 1: SELF EVALUATION TEST

Find $n,$ if $5 P(4,n)=6 P(5,n-1)$.

How many numbers greater than $20,000$ can be formed by using the digits $0, 1, 2, 3, 4$ if no digit being repeated in any number? 

How many different words can be formed from the letters of the word $ORDINATE$, so that the vowels occupy odd places? 

Out of $5$ men and $2$ women a committee of $3$ persons is to be formed so that at least one woman is to be included. How many ways committee can be formed? 

Out of $18$ points in a plane, no three are in the same line except $5$ points which are collinear. How many straight lines can be formed by joining them?

Out of $18$ points in a plane, no three are in the same line except $5$ points which are collinear. How many triangles can be formed by joining them?

A box contains $5$ different red balls and $6$ different white balls. In how many ways can $6$ be selected so that so that there are at least two balls of the same colour?

Find $n$ if ${}^{2n}C_3{:}^n{C}_3=11:1$