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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
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INTRODUCTION OF COMBINATIONS is considered one the most difficult concept.
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179 Questions around this concept.
Solve by difficulty
The value of 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 and
, determine the values of n and r.
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${ }^{n-1} C_r=\left(k^2-8\right)^n C_{r+1}$ 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?
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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Try NowA box contains 5 different coloured marbles: red, blue, green, yellow, and orange. If you want to select 2 marbles from the box, how many different combinations of marbles can you select?
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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