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Introduction Of Combinations - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • INTRODUCTION OF COMBINATIONS is considered one the most difficult concept.

  • 200 Questions around this concept.

Solve by difficulty

The value of \sum_{r=1}^{15}r^{2}\, \left ( \frac{{}^{15}\textrm{C}_{r}}{{}^{15}\textrm{C}_{r-1}} \right ) is equal to:

n is selected from the set {1,2,3......49} and the number 2n+3n+5n is formed. Total number of ways of selecting n so that the formed number is divisible by 4 is equal to

If \mathrm{ n C r: n C r+1=1: 4} and \mathrm{ n C r+1: n C r+2=4: 5}, determine the values of n and r.

${ }^{n-1} C_r=\left(k^2-8\right)^n C_{r+1}$ if and only if:

 

Let $\alpha=\frac{(4 !) !}{(4 !)^{3 !}}$ and $\beta=\frac{(5 !) !}{(5 !)^{4 !}}$ Then :

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

A bag contains 4 red balls, 3 green balls, and 2 blue balls. If you randomly select 3 balls from the bag without replacement, what is the number of possible outcomes?

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A bag contains 4 red marbles, 3 blue marbles, and 2 green marbles. If you randomly select 2 marbles from the bag without replacement, what is the number of possible outcomes?

A bakery offers 4 types of cupcakes: chocolate, vanilla, strawberry, and lemon. If a customer wants to choose 2 cupcakes for a special offer, how many different combinations of cupcakes can they select?

 

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A box contains 3 white, 4 black, and 5 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

Concepts Covered - 1

INTRODUCTION OF COMBINATIONS

So far our task was always to “arrange” objects i.e. to place them in a specific order among themselves.

Sometimes we would be interested in only “selecting” a few objects out of the given objects. In this case, we just need to “select” and we do not need to “arrange” them in an order. 

The notation of selecting r objects from n given object is ${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}$.

${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}} = \frac{n!}{(n-r)!\cdot r!}$

Multiplication Rule

If a certain work W can be completed by doing 2 tasks, first doing task A AND then doing task B.  A can be done in m ways and following that B can be done in n ways, then the number of ways of doing the work W is (m x n) ways. 

Addition Rule

If work W can be completed by doing task A OR task B, and A can be done in m ways and B can be done in n ways (and both cannot occur simultaneously: in this case we call tasks A and B as mutually exclusive), then work W can be done in (m + n) ways.

 

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INTRODUCTION OF COMBINATIONS

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