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*Q1.There are 12 students in a class. If a group of 5 students has to be selected from the class in such a way that one particular student is always included, in how many different ways can the selection be made?*

*(1) 210 (2) 220 (3) 320 (4) 330 (5) 420*

*Q2. Letters of the word “SERIES” are arranged in such a way that all the vowels always come together. What is the total number of ways of making such an arrangement?*

*(1) 720 (2) 180 (3) 144 (4) 72 (5) 36*

*Q3. 18 persons are sitting around a circular table. In how many ways can they be seated if six*

*particular persons are to always sit together?*

*(1) 18! × 6! (2) 17! × 5! (3) 13! × 6! (4) 12! × 6! (5) 12! × 5!*

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*Q4. In how many ways can the letters of the word “PRODUCT” be arranged so that all the vowels never come together?*

*(1) 5040 (2) 720 (3) 4320 (4) 1440 (5) 3600*

*Q5. There are seven boys and four girls in a row. In how many ways can they be seated in the row so that all the girls do not sit together?*

*(1) 7! × 4! (2) 11! – 7! × 4! (3) 11! – 7! (4) 11! – 4! (5) 11! – 8! × 4!*

Q6. In how many ways can 6 boys and 5 girls be seated in a row so that they sit alternately?

*(1) 43200 (2) 86400 (3) 21600 (4) 840 (5) 720*

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*Q7. In how many different ways can the letters of the word “PRODUCTION’ be arranged so that the vowels always come together?*

*(1) 15120 (2) 30240 (3) 60480 (4) 120960 (5) *

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*Q8. From a group of 8 men and 5 women, in how many different ways can six of them be included so that at least one woman is chosen?*

*(1) 1715 (2) 1688 (3) 896 (4) 996 (5) 1714*

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*Q9. In how many ways can you choose a group of four persons out of three girls and seven boys such that the group has only one girl?*

*(1) 105 (2) 210 (3) 120 (4) 224 (5) 240*

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*Q10.* *In a party, every person shakes hands with every other person. If there occur a total of 351 handshakes in the party, how many persons were present at the party?*

*(1) 25 (2) 26 (3) 27 (4) 28 (5) 29*