A student is asked to answer 10 out of 13 questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is
A student is asked to answer 10 out of 13 questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is
186
176
286
196
The Correct Option is D
Solution and Explanation
The correct option is (D) 196.
(i) Choosing 4 out of the first five questions and 6 out of the remaining 8 questions. Therefore, the number of choices in this case is given by 5C4×8C6=5C1×8C2=5×8×1×27=140.
(ii) Choosing 5 out of the first five questions and 5 out of the remaining 8 questions. This leads to 5C5×8C5=1×8C3=5×8×1×2×37=56.
Hence, the total number of choices is 140+56=196140+56=196.
Top Questions on Combinations
- A group of 9 students, s1, s2,…., s9, is to be divided to form three teams X, Y and Z of sizes 2, 3, and 4, respectively. Suppose that s1 cannot be selected for the team X and s2 cannot be selected for the team Y. Then the number of ways to form such teams, is _______.
- JEE Advanced - 2024
- Mathematics
- Combinations
- Suppose $\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}$ Then the value of $\alpha$ is
- JEE Main - 2023
- Mathematics
- Combinations
Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1,2 , 3 and 5 , and are divisible by 15 , is equal to _____
- JEE Main - 2023
- Mathematics
- Combinations
- The value of $\displaystyle\sum_{r=0}^{22}{ }^{22} C_r{ }^{23} C_r$ is
- JEE Main - 2023
- Mathematics
- Combinations
There are 10 points in a plane, of which no three points are colinear expect 4. Then the number of distinct triangles that can be formed by joining any three points of these ten points, such that at least one of the vertices of every triangle formed is from the given 4 colinear points is
- TS EAMCET - 2023
- Mathematics
- Combinations
Questions Asked in TS EAMCET exam
The ratio of the radii of two solid spheres of same mass in 2:3. The ratio of the moments of inertia of the spheres about their diameters is:
- TS EAMCET - 2023
- rotational motion
If (-c, c) is the set of all values of x for which the expansion is (7 - 5x)-2/3 is valid, then 5c + 7 =
- TS EAMCET - 2023
- Algebra of Complex Numbers
The general solution of the differential equation (x2 + 2)dy +2xydx = ex(x2+2)dx is
- TS EAMCET - 2023
- Differential equations
If i=√-1 then
\[Arg\left[ \frac{(1+i)^{2025}}{1+i^{2022}} \right] =\]- TS EAMCET - 2023
- Trigonometric Identities
If nCr denotes the number of combinations of n distinct things taken r at a time, then the domain of the function g (x)= (16-x)C(2x-1) is
- TS EAMCET - 2023
- permutations and combinations
Concepts Used:
Combinations
The method of forming subsets by selecting data from a larger set in a way that the selection order does not matter is called the combination.
- It means the combination of about ‘n’ things taken ‘k’ at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.
- For example, Imagine you go to a restaurant and order some soup.
- Five toppings can complement the soup, namely:
- croutons,
- orange zest,
- grated cheese,
- chopped herbs,
- fried noodles.
But you are only allowed to pick three.
- There can be several ways in which you can enhance your soup with savory.
- The selection of three toppings (subset) from the five toppings (larger set) is called a combination.
Use of Combinations:
It is used for a group of data (where the order of data doesn’t matter).