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A natural number n such that n! ends in exactly 1000  zeros is

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Important Questions on Permutations and Combinations

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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The largest non-negative integer k such that 24k divides 13! is
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
If *=+, /=-,+=*,-=/ then 43×561+500-100/10=?$43^{*} 561+500-100 / 10=?$
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , is
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The number of integers greater than 6000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition is 
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
If ∑r=110r!r3+6r2+2r+5=α11!, then the value of α is equal to ___ .
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The largest natural number n such that 3n divides 66! is _______
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The exponent of 6 in 72! is
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The number of 5 digit numbers which are divisible by 4, with digits from the set {1,2,3,4,5} and the repetition of digits is allowed, is _____.
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The largest power of 2 that divides 200!100! is
HARD
Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
Among the inequalities below, which ones are true for all natural numbers n greater than 1000 ?
I. n!≤nn
II. n!2≤nn
III. 10n≤n!
IV. nn≤2n!
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
How many natural numbers n are there such that n!+10 is a perfect square ?
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
If 500!=2nx is an integer, then
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
Let M=a1, a2, a3:ai∈1, 2, 3, 4, a1+a2+a3=6. Then the number of elements in M is
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The number of distinct primes dividing 12!+13!+14! Is
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The number of natural numbers less than 7000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to:
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is :
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
The remainder when x=1!+2!+3!+.....+100! is divided by 240, is
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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting

The missing value in the following figure is

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Mathematics>Algebra>Permutations and Combinations>Fundamental Principle of Counting
For which value of n∈N, n! has 13 trailing zeros?