Quant Quiz

Directions (Q. 1 – 5): Consider the arrangements of the letters of the word RAINBOW.

1. In how many ways can the letters be arranged?
(a) 5040
(b) 4050
(c) 3040
(d) 8040
(e) None of these


2. How many words begin with R?
(a) 720
(b) 360
(c) 1440
(d) 1080
(e) None of these

3. How many words begin with R and ends with W?
(a) 120
(b) 240
(c) 180
(d) 360
(e) None of these

4. How many words are there in which R and W are at the end positions?
(a) 120
(b) 180
(c) 210
(d) 240
(e) None of these

5. How many words are there in which N and B are together?
(a) 720
(b) 360
(c) 540
(d) 1440
(e) None of these

Answers
1. There are 7 letters in the word RAINBOW and each letter is used only once. So all the 7 letters can be arranged in 7! Ways.
7! = 7×6×5×4×3×2×1 = 5040.

2. If we fix R as the initial letter, then we have to arrange only 6 remaining letters.
Hence required number of permutations = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

3. If we fix R and W as the first and last letters then we have to arrange only 5 remaining letters which can be arranged in 5! = 120 ways.

4. When R and W are the first and last letters of all the words then we can arrange them in 5! Ways. Similarly when W and R are the first and last letters of the words then the remaining letters can be arrange in 5! Ways.
Thus the total number of permutations = 2 × 5! = 2 × 120 = 240 Alternatively: Except to R and W all the remaining 5 letters can be arranged in 5! Ways and R and W can be arranged in 2! Ways at the end positions. The total number of permutations = 2! × 5! = 2×120 = 240

5. Assume N and B as a single letter, then we have only 6 letters for the arrangement
i.e., A, I, R, O, W, BN which can be arranged in 6! Ways. Now B and N can also be mutually arranged in 2! Ways Therefore total number of arrangements = 2! × 6! = 2 × 720 = 1140

Directions (Q. 1 – 5): Consider the arrangements of the letters of the word RAINBOW.

1. In how many ways can the letters be arranged?
(a) 5040
(b) 4050
(c) 3040
(d) 8040
(e) None of these


2. How many words begin with R?
(a) 720
(b) 360
(c) 1440
(d) 1080
(e) None of these

3. How many words begin with R and ends with W?
(a) 120
(b) 240
(c) 180
(d) 360
(e) None of these

4. How many words are there in which R and W are at the end positions?
(a) 120
(b) 180
(c) 210
(d) 240
(e) None of these

5. How many words are there in which N and B are together?
(a) 720
(b) 360
(c) 540
(d) 1440
(e) None of these

Answers
1. There are 7 letters in the word RAINBOW and each letter is used only once. So all the 7 letters can be arranged in 7! Ways.
7! = 7×6×5×4×3×2×1 = 5040.

2. If we fix R as the initial letter, then we have to arrange only 6 remaining letters.
Hence required number of permutations = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

3. If we fix R and W as the first and last letters then we have to arrange only 5 remaining letters which can be arranged in 5! = 120 ways.

4. When R and W are the first and last letters of all the words then we can arrange them in 5! Ways. Similarly when W and R are the first and last letters of the words then the remaining letters can be arrange in 5! Ways.
Thus the total number of permutations = 2 × 5! = 2 × 120 = 240 Alternatively: Except to R and W all the remaining 5 letters can be arranged in 5! Ways and R and W can be arranged in 2! Ways at the end positions. The total number of permutations = 2! × 5! = 2×120 = 240

5. Assume N and B as a single letter, then we have only 6 letters for the arrangement
i.e., A, I, R, O, W, BN which can be arranged in 6! Ways. Now B and N can also be mutually arranged in 2! Ways Therefore total number of arrangements = 2! × 6! = 2 × 720 = 1140