In how many ways can the letters of the word PERMUTATIONS can be arranged if the

(i) Words start with P and end with S.

(ii) Vowels are all together.

(iii) There are always 4 letters between P and S?

How many chords can be drawn through 21 points on a circle?

In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls.

5.Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls each colour.

6.Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

In how many ways can one select a cricket team of 11 from 17 players in which 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected

how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that vowels and consonants occur together?

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of :

(i) exactly 3 girls? (ii) at least 3 girls? (iii) at most 3 girls?