Permutation and combination practice · Mixed difficulty

If ${P_m}$ stands for ${\;^m}{P_m}$, then $1 + 1{P_1} + 2{P_2} + 3{P_3} + ... + n.{P_n}$ is equal to

$2 m$ white counters and $2 n$ red counters are arranged in a straight line with $(m+n)$ counters on each side of a central mark. The number of ways of arranging the counters, so that the arrangements are symmetrical with respect to the central mark, is

Number of ways of selection of 4 letters of the word "PERFECT" is

The value of ${2^n}\left[ {1.3.5 \ldots \left( {2n - 3} \right)\left( {2n - 1} \right)} \right]$ is

The number of words which can be made out of the letters of the word “MOBILE” when consonants always occupy odd places, is

There are stalls for 10 animals in a ship. The number of ways the shipload can be made if there are cows, calves and horses to be transported, animals of each kind being not less than 10 , is

The number of ways of arranging $m$ numbers out of $1,2,3, \ldots, n$, so that maximum is $(n-2)$ and minimum is 2 (repetitions of numbers is allowed) such that maximum and minimum both occur exactly once $(n > 5, m > 3)$, is

How many words can be formed by using 2 consonant and 2 vowels from the word. 'TOMORROW'.

The number of ways in which 10 candidates $A_1, A_2, \ldots$, $A_{10}$ can be ranked so that $A_1$ is always above $A_2$, is

If ${\;^{18}}{C_{15}} + 2\left( {{\;^{18}}{C_{16}}} \right) + {\;^{17}}{C_{16}} + 1 = {\;^n}{C_3}$, then $n$ is equal to

In a group of 8 girls, two girls are sisters. The number of ways in which the girls can sit in a row so that two sisters are not sitting together is

Given that $\mathrm{n}$ is odd, the number of ways in which three numbers in A.P. can be selected from $1,2,3, \ldots . \mathrm{n}$ is

The number of ways in which 10 examination papers can be arranged so that the best and the worst papers never come together, is

The number of mappings (functions) from the set $A = \left\{ {1,\;2,\;3} \right\}$ into the set $B = \left\{ {1,\;2,\;3,\;4,\;5,\;6,\;7} \right\}$ such that $f\left( i \right) \le f\left( j \right)$ whenever $i < j$, is

${S_1},\;{S_2}, \ldots ,{S_{10}}$ are the speakers in a conference. If ${S_1}$ addresses only after ${S_2}$, then the number of ways the speakers address is

4 buses runs between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by another bus, then the total possible ways are

Total number of words that can be formed using the alpha- bets of the word 'KUBER', so that no alphabet is repeated in any of the formed word, is equal to

A delegation of five students is to be formed from a group of 10 students. If three particular students want to remain together whereas two particular students do not want to remain together, then the number of selection is

The number of permutations of $n$ different objects taken $r(\geq 3)$ at a time which include 3 particular objects, is

Rakshit is allowed to select 1 or more books out of $(2 n+1)$ distinct books. If the number of ways in which he may not select all of them is 126, then value of ${n}$ is ___.

If $E=\frac{1}{4} \cdot \frac{2}{6} \cdot \frac{3}{8} \cdot \frac{4}{10} \ldots \frac{30}{62} \cdot \frac{31}{64}=8^x$, then value of $x$ is

The number of all the possible selections which a student can make for answering one or more questions out of eight given questions in a paper, when each question has an alternative is

Find the no. of Permutations of all the letters of the word MATHEMATICS which starts with consonants only

A man has got seven friends. The number of ways in which he can invite one or more of his friends to dinner, is

If ${ }^n C_{r-1}=\left(k^2-8\right)\left({ }^{n+1} C_r\right)$, then $k$ belongs to

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number is

If ${ }^{m+n} P_2=90$ and ${ }^{m-n} P_2=30,$ then $(m, n)$ is given by

The number of 5 digits telephone number having at least one of their digits repeated, is

9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is

The number of different permutations of the word ‘BANANA’ is