Permutation and combination practice · Easy

The exponent of 3 in 100 !, is

There are 10 true-false questions. The number of ways, in which they can be answered is

The value of ${ }^{10} C_5 /{ }^{11} C_6$, when numerator and denominator takes their greatest value, is

If all permutations of the letters of the word PENCIL are arranged as in a dictionary, then 413th word is

A seven-digit numbers divisible by 9 is to be formed by using 7 out of numbers $\{1,2,3,4,5, 6,7,8,9\}$. The number of ways in which this can be done, is

How many four digit numbers can be formed using the digits 1, 2, 3, 4, 5 such that at least one of the digit is repeated?

A dictionary is printed consisting of 7 letters words only that can be made with a letters of the word CRICKET. If the words are printed at the alphabetical order as in an ordinary dictionary, then the number of words before the word CRICKET is

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 ways in which $p$ positive and $n$ negative signs may be placed in a row so that no two negative signs shall be together is

The number of 6 digits numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated, is

Let $S$ be the set of all functions from the set $A$ to the set $A$. If $n(A)=k$, then $n(S)$ is

If ${ }^{10} C_{{r}-1} > 2\left({ }^{10} C_{\mathrm{r}}\right)$ then $r$ is equal to

If $x \in {N}$ and $\frac{(2 x) !}{3 !(2 x-3) !}: \frac{x !}{2 !(x-2)}=44: 3$, then $x$ is equal to

A basket ball team consists of 12 pairs of twin brothers. On the first day of training, all 24 players stand in a circle in such a way that all pairs of twin brothers are neighbours. Number of ways this can be done is :

Consider the following statement:

1.The number of ways of arranging m different things taken all at a time in which $p \leqslant m$ perticular things are never together is $m! - \left( {m - p + 1} \right)!p!$

2. A pack of 52 cards can be divided equally among four players in order in $\frac{{52!}}{{{{\left( {13!} \right)}^4}}}$ ways

Which of these is/are correct?

The number of ways distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

A man has three friends. The number of ways he can invite one friend everyday for dinner on six successive nights, so that no friend is invited more than three times, is

The number of arrangements which can be made out of the letters of the word ALGEBRA, without changing the relative order (positions) of vowels and consonants, is

Eleven books consisting of 5 Mathematics, 4 physics and 2 Chemistry are places on a shelf. The number of possible ways of arranging them on the assumption that the books of the same subject are all together, is

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

The number of ways in which $n$ things of which $r$ are alike, can be arranged in a circular order, is

Four married couples are to be seated in a row having 8 chairs. The number of ways so that spouses are seated next to each other, is

The value of $\sum \limits_{r = 1}^n \,\frac{{{\;^n}{P_r}}}{{r!}}$ is

A man has 6 friends. In how many ways he can invite one or more of them at dinner?

Find the number of ways of arranging the letters of the word ENGINEERING

From 7 gentlemen and 4 ladies, a committee of 5 is to be formed. The number of ways in which this can be done so as to include atleast one lady is

If one test (on screening paper basis) was conducted on Batch A, maximum number of marks is $(90 \times 3)=270.4$ students get the marks lower than 80 . Coaching institute decide to inform their guardians, that is why their result card were sent to their home. The number of ways, in which all the letters were put in wrong envelopes, is

How many 10 digit numbers can be written by using the digits 1 and 2?

If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent. The number of points in which they intersect each other is

The number of ways 12 different books can be distributed equally among 4 persons, is