Permutation and combination practice · Easy

The number of ways in which three girls and nine boys can be seated in two cars, each having numbered seats, 3 in the front and 4 at the back, is

There are 5 historical moments, 6 gardens and 7 shopping malls in the city. In how many ways a tourist can visit the city, if he visits at least one shopping mall?

The total number of ways in which 4 boys and 4 girls can form a line, with boys and girls alternating, is

Nine hundred distinct $\mathrm{n}$-digit number $\mathrm{s}$ are to be forme using exactly the three digits. 2, 5 and 7 . The smallest value  of $\mathrm{n}$ for which this is possible is.

A gentleman invites 13 guests to a dinner and places 8 of them at one table and remaining 5 at the other, the tables being round. The number of ways he can arrange the guests is

The sum of the digits in the unit place of all numbers formed with the help of 3, 4, 5, 6 taken al, at a time, is

The total number of natural numbers of six digits that can be made with digits 1,2,3,4, if all digits are to appear in the same number at least once, is

The number of numbers less than 1000 that can be formed out of the digits $0,1,2,3,4$ and 5 , no digit being repeated, is

The number of all four digit numbers which are divisible by 4 that can be formed from the digits 1,2,3,4 and 5 is

The number of ways in which the letters of the word 'SUCCESSFUL' be arranged such that the S's and U's will come together is

The number of numbers, strictly between 5000 and 10000 can be formed using the digits $1,3,5,7,9$ without repetition, is

There are 20 students in a class, in which 12 boys and 8 girls. The class teacher select either a boy or a girl for monitor of the class. In how many ways, the teacher can make this selection?

The number of 9 digit numbers which have all distinct digits, is

The last digit of $(1 !+2 !+\ldots \ldots+2009 !)^{500}$ is

In how many ways the letters of the word ENGINEERING, can be arranged such that all E's come together but no two N's come together

The number of arrangements that can be formed out of 'LOGARITHM' so that "No two vowels come together is

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

The number of different matrices that can be formed with elements $0,1,2$ or $3,$ each matrix having 4 elements, is

How many numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition of digits is allowed)?

The number of arrangements that can be formed out of GANESHPURI so that "The letter 'G' always occurs in first place is

If the letters of the word MOTHER are written in all possible orders and these words are written out as in a dictionary then the rank of the word MOTHER is

The number of ways of choosing triplets $(x, y, z)$ such that $z \geq \max \{x, y\}$ and $x, y, z \in\{1,2, \ldots, n, n+1\}$, is

The sum of all four digit numbers that can be formed by using digits $2,4,6,8$ (when repetition of digits is not allowed) is

If ${\;^{12}}{P_r} = 1320$, then $r$ is equal to

The number of ways in which the letters of the word BALLOON can be arranged so that two L's do not come together, is

At an election, a voter may vote for any number of candidates not greater than the number to be chosen. There are 10 candidates and 5 members to be selected. The number of ways of in which a voter can vote is:

The number of numbers that can be formed by using digits 1,2,3,4,3,2,1 so that odd digits always occupy odd places

If ${\;^{n + 2}}{C_8}\;:{\;^{n - 2}}{P_4} = 57\;:16,$ then the value of $n$ is

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

Ashok, Usha, Rani, Sonu are to give speeches in a class. The teacher can arrange the order of their presentation in