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Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

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Important Questions on Permutations & Combinations

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CAT
IMPORTANT
Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 64
Romeo and Juliet write love-letters to none but to each other. In a given period of time, Romeo writes 4 letters and Juliet writes 2 letters. During this period, at any given point of time Romeo writes greater than or equal to the number of letters written by Juliet. Find the number of ways of writing love-letters to each other,
MEDIUM
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 65
Malvika wants to colour a cubical box from outside. In how many ways can she colour it if she wants to colour each face of the box with either blue or pink colour?
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 66
A gym opens twice a day - morning and evening. But, I don't work out twice a day. I attend it only 4 times a week. In how many ways can I attend the gym in a week?
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 67
An n-digit number is a positive number with exactly n-digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2,5 and 7. The smallest value of n for which this is possible is
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 68
Which of the following is not a possible number of regions into which three straight lines, of infinite extent, divide a plane?
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 69
If you travel between Mumbai and Pune, you have to go through a 10 km long tunnel. Lately there has been a surge in the incidents of loot and plunder and many passengers have been harassed and injured inside the tunnel. Considering the enormity of the law and order problem, highway police decided to establish 4 security posts in order to ensure the safety of life and luggage of commuters. The minimum distance between any two posts is 1 km. Each security post must be n km (n=0,1,2,3…) apart from entry/exit of the tunnel and none of them will be outside the tunnel. Find the number of ways of selecting the spots for upcoming security posts.
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 70
A rectangle with sides (2 m-1) and (2 n-1) is divided into squares of unit length by drawing parallel lines as shown in the diagram, then the number of rectangles possible with odd side lengths is
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CAT
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 71
A black ant has to go from the origin to a point (6,4) on the Cartesian plane, using the coordinate axes. However, it avoids crossing the point (4,1), as a red ant is sitting there. Find the total number of shortest paths that it can go along.