Permutations and Combinations · Mathematics · COMEDK
MCQ (Single Correct Answer)
A coach needs to select a $\mathbf{4}$-player starting lineup from a pool of $\mathbf{1 0}$ players:
5 guards
3 forwards
2 centres
Find the number of different selections if the 4-player starting lineup must include:
At least 1 guard
At most 1 forward
Exactly 1 centre
$$ \text { If }{ }^{\mathrm{n}} C_{13},{ }^{\mathrm{n}} C_{14} \text { and }{ }^{\mathrm{n}} C_{15} \text { are in arithmetic progression, then the positive integer value of ' } \mathbf{n} \text { ' can be } $$
In how many ways can the squares of a $\mathbf{4} \times \mathbf{2}$ grid ( 4 rows and 2 columns) be filled with the letters of the word 'SPHERE' such that each row contains at least one letter?
A batch of $\mathbf{1 0}$ cupcakes consists of $\mathbf{5}$ chocolate, $\mathbf{3}$ vanilla, and $\mathbf{2}$ strawberry. If 4 cupcakes are selected to be put into a gift box, find the number of different ways they can be chosen if the selection must include at least $\mathbf{2}$ chocolate, at most $\mathbf{1}$ vanilla, and exactly $\mathbf{1}$ strawberry cupcake.
The range of the function $f(x)={ }^{(7-x)} P_{(x-3)}$ is
For an examination a candidate has to select 7 questions from three different groups $$\mathrm{A}, \mathrm{B}$$ and C. The three groups contain 4, 5 and 6 questions respectively. In how many different ways can a candidate make his selection if he has to select atleast 2 questions from each group?
The letters of the word "COCHIN" are permuted and all the permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word "COCHIN" is
The number of four digit numbers strictly greater than 4321 formed using the digits $$0,1,2,3,4,5$$ with repetition of digit is
A student has 3 library cards and 8 books of his interest in the library. Out of these 8 books he does not want to borrow Chemistry part 2 unless he can borrow Chemistry part 1 also. In how many ways can he choose the three books to be borrowed?
In how many ways can the word "CHRISTMAS" be arranged so that the letters '$$\mathrm{C}$$' and '$$\mathrm{M}$$' are never adjacent?
If $$\left[{ }^{n+1} C_{r+1}\right]:\left[{ }^n C_r\right]:\left[{ }^{n-1} C_{r-1}\right]=11: 6: 3$$ then $$n r=$$
$$\text { Find }{ }^n C_{21} \text {, if }{ }^n C_{10}={ }^n C_{12}$$
There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any two of them?
The total number of numbers greater than 1000 but less than 4000 that can be formed using 0, 2, 3, 4 (using repetition allowed) are
A polygon of n sides has 105 diagonals, then n is equal to
How many factors of $$2^5 \times 3^6 \times 5^2$$ are perfect squares?
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. The number of ways in which he can choose the 7 question is
In a 12 storey house, 10 people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2, 3 & 5 people at different storeys. The number of ways they can do so if the lift does not stop up to the second storey is
$$(2^{3n}-1)$$ is divisible by
$$\sum\limits_{n = 1}^m {n\,.\,n!} $$ is equal to
If nC3 = 220, then n = ?
There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?
A regular polygon of n sides has 170 diagonals, then n is equal to
The value of $$1\,.\,1! + 2\,.\,2! + 3\,.\,3! + \,...\, + \,n\,.\,n!$$ is
The number of triangles which can be formed by using the vertices of a regular polygon of $$(n+3)$$ sides is 220. Then, $$n$$ is equal to
Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points?
How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7?
If a polygon of n sides has 275 diagonals, then n is equal to
The number of positive divisors of 252 is
The remainder obtained when 5124 is divided by 124 is