In an examination of Mathematics paper, there are $20$ questions of equal marks and the question paper is divided into three sections : $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. A student is required to attempt total $15$ questions taking at least $4$ questions from each section. If section $A$ has $8$questions, section $\mathrm{B}$ has $6$ questions and section $\mathrm{C}$ has $6$ questions, then the total number of ways a student can select $15$ questions is
In an examination of Mathematics paper, there are $20$ questions of equal marks and the question paper is divided into three sections : $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. A student is required to attempt total $15$ questions taking at least $4$ questions from each section. If section $A$ has $8$questions, section $\mathrm{B}$ has $6$ questions and section $\mathrm{C}$ has $6$ questions, then the total number of ways a student can select $15$ questions is
- [JEE MAIN 2024]
- A
$11370$
- B
$11376$
- C
$11375$
- D
$11350$
Similar Questions
Suppose Anil's mother wants to give $5$ whole fruits to Anil from a basket of $7$ red apples, $5$ white apples and $8$ oranges. If in the selected $5$ fruits, at least $2$ orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer $5$ fruits to Anil is $........$
Suppose Anil's mother wants to give $5$ whole fruits to Anil from a basket of $7$ red apples, $5$ white apples and $8$ oranges. If in the selected $5$ fruits, at least $2$ orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer $5$ fruits to Anil is $........$
- [JEE MAIN 2023]
If ${ }^{1} \mathrm{P}_{1}+2 \cdot{ }^{2} \mathrm{P}_{2}+3 \cdot{ }^{3} \mathrm{P}_{3}+\ldots+15 \cdot{ }^{15} \mathrm{P}_{15}={ }^{\mathrm{q}} \mathrm{P}_{\mathrm{r}}-\mathrm{s}, 0 \leq \mathrm{s} \leq 1$ then ${ }^{\mathrm{q}+\mathrm{s}} \mathrm{C}_{\mathrm{r}-\mathrm{s}}$ is equal to .... .
If ${ }^{1} \mathrm{P}_{1}+2 \cdot{ }^{2} \mathrm{P}_{2}+3 \cdot{ }^{3} \mathrm{P}_{3}+\ldots+15 \cdot{ }^{15} \mathrm{P}_{15}={ }^{\mathrm{q}} \mathrm{P}_{\mathrm{r}}-\mathrm{s}, 0 \leq \mathrm{s} \leq 1$ then ${ }^{\mathrm{q}+\mathrm{s}} \mathrm{C}_{\mathrm{r}-\mathrm{s}}$ is equal to .... .
- [JEE MAIN 2021]
Find the number of words with or without meaning which can be made using all the letters of the word $AGAIN$. If these words are written as in a dictionary, what will be the $50^{\text {th }}$ word?
Find the number of words with or without meaning which can be made using all the letters of the word $AGAIN$. If these words are written as in a dictionary, what will be the $50^{\text {th }}$ word?
A committee of $12$ is to be formed from $9$ women and $8$ men in which at least $5$ women have to be included in a committee. Then the number of committees in which the women are in majority and men are in majority are respectively
A committee of $12$ is to be formed from $9$ women and $8$ men in which at least $5$ women have to be included in a committee. Then the number of committees in which the women are in majority and men are in majority are respectively
- [IIT 1994]
In a shop there are five types of ice-creams available. A child buys six ice-creams.
Statement $-1 :$ The number of different ways the child can buy the six ice-creams is $^{10}C_5.$
Statement $-2 :$ The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging $6 \,A's$ and $4 \,B's$ in a row.
In a shop there are five types of ice-creams available. A child buys six ice-creams.
Statement $-1 :$ The number of different ways the child can buy the six ice-creams is $^{10}C_5.$
Statement $-2 :$ The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging $6 \,A's$ and $4 \,B's$ in a row.
- [AIEEE 2008]