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- Permutation and Combination
1.
There are 5 red, 4 white and 3 blue marbles in a bag. They are taken out one by one and arranged in a row. Assuming that all the 12 marbles are drawn, find the number of different arrangements?
- A.27207
- C.27270
- B.27720
- D.22077
- Answer & Explanation
- Report
Answer : [B]
Explanation :
Explanation :
| Total number of balls = 12 | ||||||||
| Of these 5 balls are of 1st type (red color), 4 balls are of 2nd type and 3 balls are of 3rd type. | ||||||||
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2.
There are 5 different shades of green dye, 4 different shades of blue dye and 3 different shades of red dye. If at least one green and one blue has to be included, how many combinations of dye are possible?
- A.7320
- C.3270
- B.3720
- D.3702
- Answer & Explanation
- Report
Answer : [B]
Explanation :
Explanation :
| From the 5 different shades of green, one or more shades can be chosen in | ||||
| 5C1 + 5C2 + 5C3 + 5C4 + 5C5 = 31 ways | ||||
| From 4 different shades of blue, one or more can be chosen in | ||||
| 4C1 + 4C2 + 4C3 + 4C4 = 15 ways | ||||
| Similarly, from 3 different shades of red one or more or none can be taken in | ||||
| 3C3 + 3C2 + 3C1 + 3C0 = 8 | ||||
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3.
A set of seven parallel lines is interested by another set of five parallel lines. How many parallelograms are formed by this process?
- A.280
- C.210
- B.140
- D.60
- Answer & Explanation
- Report
Answer : [C]
Explanation :
Explanation :
| Any two parallel lines from the first set and any two from the second set will form a parallelogram. |
| The number of parallelograms that are formed = 7C2 x 5C2 = 21 x 10 = 210 |
4.
In how many ways can the word, ‘RESHMA’ be arranged, so that each word begins with R and ends with M?
- A.6!
- C.24
- B.25
- D.20
- Answer & Explanation
- Report
Answer : [C]
Explanation :
Explanation :
| Here the word is to begin with R and to end with M. So, the two places of the word is fixed. |
| Hence, remaining 4 places can be filled with 4 words in 4! Ways. |
| Required number of ways = 4! = 24 ways |
5.
In an examination, a candidate has to pass in each of the 6 subjects. In how many ways can he fail?
- A.63
- C.6!
- B.26
- D.6
- Answer & Explanation
- Report
Answer : [A]
Explanation :
Explanation :
| The student can fail in the 6 subjects in any of the following ways. | |||||||||||||||||
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