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
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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.
Required number of arrangements =
 12! 5!4!3!
= 27720
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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
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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
 The total number of ways = 31 x 15 x 8 = 3720 ways
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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
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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
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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
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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
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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