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!

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

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)

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

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

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