Two numbers are: a= 3607 and b= 2601

Important Questions on Permutation and Combination

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

The largest non-negative integer $k$ such that ${24}^k$ divides $13!$ is

EASY

Mathematics>Algebra>Permutation and Combination>Factorial Notation

If $*=+, /=-,+=*,-=/$ then $43\times 561+500-100/10=?$$43^{*} 561+500-100 / 10=?$

EASY

Mathematics>Algebra>Permutation and Combination>Factorial Notation

The exponent of $6$ in $72!$ is

EASY

Mathematics>Algebra>Permutation and Combination>Factorial Notation

The largest natural number $n$ such that $3^n$ divides $66!$ is $\_\_\_\_\_\_\_$

HARD

Mathematics>Algebra>Permutation and Combination>Factorial Notation

If $\sum _{r=1}^{10}r!\left(r^3+6r^2+2r+5\right)=\alpha \left(11!\right)$, then the value of $\alpha$ is equal to ___ .

HARD

Mathematics>Algebra>Permutation and Combination>Factorial Notation

The number of $3$ digit numbers, that are divisible by either $3$ or $4$ but not divisible by $48$ , is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

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

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

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:

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

The largest power of $2$ that divides $\frac{200!}{100!}$ is

HARD

Mathematics>Algebra>Permutation and Combination>Factorial Notation

Among the inequalities below, which ones are true for all natural numbers $n$ greater than $1000$ ?
I. $n!\le n^n$
II. ${\left(n!\right)}^2\le n^n$
III. ${10}^n\le n!$
IV. $n^n\le \left(2n\right)!$

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

How many natural numbers $n$ are there such that $\mathrm{n}!+10$ is a perfect square ?

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

If $500!=2^{n}x$ is an integer, then

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

The number of integers greater than $6000$ that can be formed, using the digits $3, 5, 6, 7$ and $8$, without repetition is 

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

The number of distinct primes dividing $12!+13!+14!$ Is

EASY

Mathematics>Algebra>Permutation and Combination>Factorial Notation

Let $M=\left\{\left(a_1,a_2,a_3\right):a_i\in \left\{1,2,3,4\right\},a_1+a_2+a_3=6\right\}.$ Then the number of elements in $M$ is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

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

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

The number of $5$ digit numbers which are divisible by $4$, with digits from the set $\{\mathrm{1,2},\mathrm{3,4},5\}$ and the repetition of digits is allowed, is _____.

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

The remainder when $x=1!+2!+3!+\mathrm{.....}+100!$ is divided by $240$, is

EASY

Mathematics>Algebra>Permutation and Combination>Factorial Notation

The missing value in the following figure is

MEDIUM

Mathematics>Algebra>Permutation and Combination>Factorial Notation

For which value of $n\in N, n!$ has $13$ trailing zeros?