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The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is

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Important Questions on Permutation and Combination

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Mathematics>Algebra>Permutation and Combination>Permutations
Ten different letters of an alphabet are given, words with five letters are formed from these given letters. Then, the number of words which have at least one letter repeated is
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Mathematics>Algebra>Permutation and Combination>Permutations
The largest non-negative integer k such that 24k divides 13! is
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Mathematics>Algebra>Permutation and Combination>Permutations
The sum of the digits in the unit's place of all the 4 - digit numbers formed by using the numbers 3, 4, 5 and 6, without repetition is :
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Mathematics>Algebra>Permutation and Combination>Permutations
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4  taken all at a time. The number of such numbers in which the odd digits occupy even places is
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Mathematics>Algebra>Permutation and Combination>Permutations
The number of all 3-digits numbers abc (in base 10) for which 10 is
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Mathematics>Algebra>Permutation and Combination>Permutations
If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is 
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Mathematics>Algebra>Permutation and Combination>Permutations
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:
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Mathematics>Algebra>Permutation and Combination>Permutations

How many numbers of four digits can be made by using the digits 3, 5, 6, 7, and 9?  (Repetition of digits is not allowed)

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Mathematics>Algebra>Permutation and Combination>Permutations
If Pr+656:Pr+3=30800:154 , then r is equal to
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Mathematics>Algebra>Permutation and Combination>Permutations
The number of distinct primes dividing 12!+13!+14! Is
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Mathematics>Algebra>Permutation and Combination>Permutations
The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is
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Mathematics>Algebra>Permutation and Combination>Permutations
Two girls and four boys are to be seated in a row in such a way that the girls do not sit together. In how many different ways can it be done?
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Mathematics>Algebra>Permutation and Combination>Permutations
The number of four-digit numbers strictly greater than 4321 that can be formed using the digit 0,1,2,3,4,5 (repetition of digits is allowed) is:
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Mathematics>Algebra>Permutation and Combination>Permutations
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:
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Mathematics>Algebra>Permutation and Combination>Permutations
The number of 6 digit number that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is:
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Mathematics>Algebra>Permutation and Combination>Permutations
The number of 4 digit numbers without repetition that can be formed using the digits 1, 2, 3, 4, 5, 6, 7 in which each number has two odd digits and two even digits is
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Mathematics>Algebra>Permutation and Combination>Permutations

In how many ways the letters of word 'MACHINE' can be arranged so that vowels will always be together?

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Mathematics>Algebra>Permutation and Combination>Permutations
How many ways are there to arrange the letters of the word EDUCATION so that all the following three conditions hold?
- the vowels occur in the same order EUAIO,
- the consonants occur in the same order DCTN,
- no two consonants are next to each other.
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Mathematics>Algebra>Permutation and Combination>Permutations
How many natural numbers n are there such that n!+10 is a perfect square ?
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Mathematics>Algebra>Permutation and Combination>Permutations
The number of ways in which 3 prizes can be distributed to 4 children, so that no child gets all the three prizes, are