Q.1. In how many ways can a cricket team of 11 players be selected out of 16 players, if two particular players are always to be selected?
Q.2. In how many ways can the letters of the word “ABACUS” be arranged such that the vowels always appear together?
Q.3. Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements
(i) do the words start with P
(ii) do all the vowels always occur together
Q.4. A committee of 5 is to be formed out of 6 gents and 4 Ladies. In how many ways this can be done, when
(i) at least two ladies are included?
(ii) at most two ladies are included?
Q.5. How many four letter words can be formed using the letters of the letters of the word ‘FAILURE’ so that
(i) F is included in each word
(ii) F is excluded in each word.
Q.6. In how many ways can the letters of the word “PENCIL” be arranged so that I is always next to L.
Q.7. How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Q.8. It is needed to seat 5 boys and 4 girls in a row so that the girl gets the even places. How many are such arrangements possible?
Q.9. Find the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
Q.10. If the letters of the word ‘PRANAV’ are arranged as in dictionary in all possible ways, then what will be 182nd word.
Q.11. Using the letters of the word, ‘ARRANGEMENT’ how many different words (using all letters at a time) can be made such that both A, both E, both R and both N occur together.
Q.12. Prove that 33! in divisible by 2¹⁵ what is the largest integer n such that 33! is divisible by 2 power of n ?
Q.13. We wish to select 6 persons from 8 but, if the person A is chosen, then B must be chosen. In how many ways can selections be made?
Q.14. Find the number of different words that can be formed from the letters of the word TRIANGLE, so that no vowels are together.
Q.15. In an election, these are ten candidates and four are to be elected. A voter may vote for any number of candidates, not greater than the number to be elected. If a voter vote for at least one candidate, then find the number of ways in which he can vote.
Q.16. Using the letters of the word 'EDUCATION' how many words using 6 letters can be made so that every word contains atleast 4 vowels?
Q.17. How many 3 letter words can be formed using the letters of the word INEFFECTIVE?
Q.18. How many different four letter words can be formed (with or without meaning) using the letters of the word “MEDITERRANEAN” such that the first letter is E and the last letter is R.
Q.19. If all letters of word ‘MOTHER’ are written in all possible orders and the word so formed are arranged in a dictionary order, then find the rank of word ‘MOTHER’?
Q.20. If nCr-1= 36 nCr = 84 and nCr+1= 126, then find the value of rC2.
Q.21. In how many ways can a football team of 11 players be selected from 16 players? How many of them will
- include 2 particular players?
- exclude 2 particular players?
Q.23. How many words, with or without meaning can be made from the letters of the word MONDAY. Assuming that no. letter is repeated, it
(i) 4 letters are used at a time
(ii) All letters are used but first letter is a vowel?
Q.24. Prove that 
Q.25. In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back? How many seating arrangements are possible if 3 girls should sit together in a back row on adjacent seats?
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