Permutation and combination practice · Easy

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

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 ___.

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 ${ }^{m+n} P_2=90$ 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

The sum of all numbers which can be formed by using the digits $1,3,5,7$ all at a time and which have no digit repeated is

The number of six digit numbers which have sum of their digits as an odd integer, is

If ${ }^{12} {P}_{{r}}-{ }^{11} {P}_6+6 .{ }^{11} {P}_5$, then ${r}$ is equal to:

The number of six digit numbers that can be formed from the digits $1,2,3,4,5,6$ and 7 , so that digits do not repeat and the terminal digits are even is

The number of points $(x, y, z)$ in space, whose each coordinate is a negative integer such that $x+y+z+12=0$, is

Letter of the word INDIANOIL are arranged in all possible ways. The number of permutations in which A, I, O occur only at odd places, is

The value of $^{50}{C_4} + \sum \limits_{r = 1}^6 \;\;{\;^{56 - r}}{C_3}\;$ is

The sum of divisors of 2520 is

The number of ways are arranging 19 persons, if two particular delegates never sit together

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

The number of zeros at the end of 100 ! Is

The total number of selections from 4 boys and 3 girls if each selection has to contain at least one boy is

The total number of 8 digits numbers which have all different digits is