Tag: factorial notation

Questions Related to factorial notation

The number of one one functions that can be defined from $A={a,b,c}$ into $B=1,2,3,4,5}$ is

exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

$^{5}{P} _{3}$
$^{5}{C} _{3}$
${5}^{3}$
${3}^{5}$

The number of ways in which $8$ different flowers can be strung to form a garland so that $4$ particulars flowers are never separated, is?

exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

$4!\cdot 4!$
$\dfrac{8!}{4!}$
$288$
None

If $\displaystyle ^{n}P _{3}:^{n}P _{6}=1:210$, find $n$.

exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

$10$
$4$
$5$
$9$

Total number of $6-$digit numbers in which all the odd digits and only odd digits appears, is

exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

$\dfrac {5}{2}(6\ !)$
$6!$
$\dfrac {1}{2}(6\ !)$
$\dfrac {3}{2}(6\ !)$

Total number of $6-$ digit numbers in which all the odd digits and only odd digits appear, is

exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

$\dfrac{5}{2}\left(6!\right)$
$6!$
$\dfrac{1}{2}\left(6!\right)$
$none$

The number of many one functions from $A=}1,2,3}$ to $B={a,b,c,d}$ is

exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

$64$
$24$
$40$
$0$

If $\displaystyle ^{n+5}P _{n+1} = \frac{11\left ( n-1 \right )}{2}.^{n+3}P _n$ then the value of n is

exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

7
8
6
5

Find the value of $n$ when:

exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

$^{n-1}P _{3}:^{n+1}P _{3}=5:12$
$^{n}P _{6}=10.^{n}P _{5}$
$^{56}P _{n+6}:^{54}P _{n+3}=30800$
$^{6+n}P _{2}:^{6+n}P _{2}=56:12$

If P(n, n) denotes the number of permutations of n different things taken all at a time then P(n, n) is also identical to

exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

n.P(n 1, n 1)
P(n, n 1)
n!
(n r) . P(n, r)

$\displaystyle ^{n}P {n}=$___.

exponent of a prime in n! factorial notation combinatorics and mathematical induction permutations and combinations maths

$n!$
$(n-1)!(3)$
$1$
$(n+1)6$