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In how many ways one black and one white rook can be placed on a chessboard so that they are never in an attacking position?

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Important Questions on Permutations & Combinations

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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 61
There are 9 pairs of white shoes and 6 pairs of black shoes contained in a box. We are allowed to draw only one shoe at a time. Minimum how many shoes are required to be drawn out to get one pair of white shoes?
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 62
In the previous question, minimum how many shoes must be drawn out to get at least 1 pair of either black or white shoes?
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 63
There are four different coloured balls and four boxes of the same colour as that of each ball is. Find the number of ways in which exactly one ball can be put in a box so that the colour of the box and that of ball is distinct.
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 64
In the previous question (no. 63) find the number of ways in which only two balls can be put in the correct boxes i.e., the colour of box and the colour of contained ball be same.
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 65
Find the number of digits required to write down the number of pages in a 300 pages book.
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 66
Find the number of numbers that can be formed using all the digits 1,2,3,4,3,2,1 only once so that the odd digits occupy odd places only.
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 83
Once Munnabhai gets admitted to a psychiatric hospital. In his room, there are two bulbs connected to two different switches, independently. One night, while accompanying him, his best buddy Circuit notices that there is, initially, no light in the room, but whenever a mosquito bites him he switches on the light and then immediately switches it off. Throughout the night, Munnabhai presses the switch (on/off) six times. Finally when Munnabhai stops playing around with the switches, Circuit notices that there is no light in the room. In how many ways Munnabhai ends up having no light in his room by pressing the given switches on or off exactly six times?
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Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 84
Mr. Been, who is getting older and senile, is standing on a crossroad totally confused about his directions. He can move in any of the four directions - North, South, East or West. He takes some steps and then comes back to the same point at the crossroad. In how many ways can he end up being at the same point where he is initially standing by taking total 8 steps?