Introduction Of Combinations - Practice Questions & MCQ

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.

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

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?