05%20-%20Permutations%20and%20Combinations

05%20-%20Permutations%20and%20Combinations - 05 -...

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05 - PERMUTATIONS AND COMBINATIONS Page 1 ( Answers at the end of all questions ) ( 1 ) If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number ( a ) 601 ( b ) 600 ( c ) 603 ( d ) 602 [ AIEEE 2005 ] ( 2 ) The value of 4 50 C + = 6 1 r 3 56 C r - is ( a ) 4 55 C ( b ) 3 55 C ( c ) 3 56 C ( d ) 4 56 C [ AIEEE 2005 ] ( 3 ) How many ways are here to arrange the letters in the word GARDEN with the vowels in alphabetical order ? ( a ) 120 ( b ) 240 ( c ) 360 (d ) 480 [ AIEEE 2004 ] ( 4 ) The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is ( a ) 5 ( b ) 21 ( c ) 3 8 ( d ) 3 8 C [ AIEEE 2004 ] ( 5 ) A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is ( a ) 140 ( b ) 196 ( c ) 280 ( d ) 346 [ AIEEE 2003 ] ( 6 ) The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by ( a ) 30 ( b ) 5 ! × 5 ! ( c ) 5 ! × 4 ! ( d ) 7 ! × 5 ! [ AIEEE 2003 ] ( 7 ) If r n C denotes the number of combinations of n things taken r at a time, then the value of expression 1 r n C + + 1 r n C - + 2 r n C is ( a ) r 2 n C + ( b ) 1 r 2 n C + + ( c ) r 1 n C + ( d ) 1 r 1 n C + + [ AIEEE 2003 ]
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05 - PERMUTATIONS AND COMBINATIONS Page 2 ( Answers at the end of all questions ) ( 8 ) If repetition of the digits is allowed, then the number of even natural numbers having three digits is ( a ) 250 ( b ) 350 ( c ) 450 ( d ) 550 [ AIEEE 2002 ] ( 9 ) If 3 1 n C + = 2 2 n C , then the value of n is ( a ) 3 ( b ) 4 ( c ) 5 ( d ) 6 [ AIEEE 2002 ] ( 10 ) If 1 r n C - = 36, r n C = 84 and 1 r n C + = 126, then n and r are respectively ( a ) 9, 6 ( b ) 9, 3 ( c ) 6, 3 ( d ) 6, 2 [ AIEEE 2002 ] ( 11 ) If ( 1 + x ) n = n n 2 2 1 0 x C ... x C x C C + + + + , then the value of 1 n n 2 3 1 2 0 1 C nC ... C
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This note was uploaded on 11/28/2011 for the course MATH 300 taught by Professor Jones during the Spring '06 term at ITT Tech Flint.

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05%20-%20Permutations%20and%20Combinations - 05 -...

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