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If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
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In how many ways can five children stand in a queue?
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From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?
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Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?
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Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?
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Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.
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How many three-digit numbers are there, with distinct digits, with each digit odd?
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How many words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?
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How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?
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There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?
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There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?
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How many three-digit numbers are there, with no digit repeated?
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How many 6-digit telephone numbers can be constructed with digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each number starts with 35 and no digit appears more than once?
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In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?
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If a denotes the number of permutations of (x + 2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x − 11 things taken all at a time such that a = 182 bc, find the value of x.
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How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
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How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?
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Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, if no digit is repeated? How many of these will be even?
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All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.
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In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?
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