There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of

Question

Match each item given under the column C1 to its correct answer given under the column C2.

(1) There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of :

| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject : | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |

(2) Five boys and five ***** form a line. Find the number of ways of making the seating arrangement under the following condition:

| (a) Boys and alternate: | (i) 5! × 6! |
| (b) No two sit together : | (ii) 10 ! – 5 ! 6 ! |
| (c) All the sit together | (iii) (5!)2 + (5!)2 |
| (d) All the are never together | (iv) 2 ! 5 ! 5 ! |

(3) There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find :

| (a) In how many ways committee can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular lecturer is excluded | (iv) 10C2 × 20C3 |

(4) Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find

| (a) how many numbers are formed? | (i) 840 |
| (b) how many numbers are exactly divisible by 2? | (ii) 200 |
| (c) how many numbers are exactly divisible by 25? | (iii) 360 |
| (d) how many of these are exactly divisble by 4? | (iv) 40 |

(5) How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |

Answer 1

(1) (a) ↔ (ii)

(b) ↔ (iii) and

(c) ↔ (i)

(2) (a) ↔ (iii)

(b) ↔ (i)

(c) ↔ (iv),

(d) ↔ (ii)

(3) (a) ↔ (iv)

(b) ↔ (iii)

(c) ↔ (ii),

(d) ↔ (i)

(4) (a) ↔ (i)

(b) ↔ (iii)

(c) ↔ (iv),

(d) ↔ (ii)

(5) (a) ↔ (iii)

(b) ↔ (i)

(c) ↔ (ii)