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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 ( 3 ) How many ways are here to arrange the letters in the word GARDEN with the vowels in alphabetical order ? ( 4 ) The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is ( 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 ( 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

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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
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