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Math Help - a few permutation problems

  1. #1
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    a few permutation problems

    Hi all!!
    please help me in solving some perm problems listed below:

    1.If in a group of 'n' distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is:
    a)10, b)8, c)6, d)none of these

    2. A 5-digit number divisible by 3 is to be formed using the digits 0,1,2,3,4 and 5 without repetition. The number of ways to do this is:
    a) 216, b)600, c)240, d)3125

    3.The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always 2 persons , is:
    a) 60*5!, b) 15*4!*5!, c) 4!*5!, d)none of these

    4.The number of arrangements of letters of the word 'BHARAT' taking 3 at a time is:
    a)72, b)120, c)14, d)none of these

    I will appreciate your time and effort .
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  2. #2
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    Quote Originally Posted by sapanjot View Post
    Hi all!!
    please help me in solving some perm problems listed below:

    1.If in a group of 'n' distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is:
    a)10, b)8, c)6, d)none of these

    Mr F says: Solve {\color{red}^n P _4 = 12 (^n P _2)} for n (or just substitute and test each option a, b and c) .....

    2. A 5-digit number divisible by 3 is to be formed using the digits 0,1,2,3,4 and 5 without repetition. The number of ways to do this is:
    a) 216, b)600, c)240, d)3125

    Mr F says: What restrictions are placed on a five digit number to make it divisible by 3 .....?

    3.The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always 2 persons , is:
    a) 60*5!, b) 15*4!*5!, c) 4!*5!, d)none of these

    Mr F says: Consider A X X B as a single unit where X represents two random people. How many ways can you make the unit A X X B .....? How many different arrangements of five objects are there?

    4.The number of arrangements of letters of the word 'BHARAT' taking 3 at a time is:
    a)72, b)120, c)14, d)none of these

    Mr F says: What's the formula for the number of arangements of r objects chosen from n when some of the objects are repeated?

    I will appreciate your time and effort .
    ..
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