$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-
$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-
- A
$^{20}C_4$
- B
$2. ^{21}C_4$
- C
$2. ^{22}C_4$
- D
$^{23}C_4$
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$^n{C_r}{ + ^n}{C_{r - 1}}$ is equal to
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In an examination, a question paper consists of $12$ questions divided into two parts i.e., Part $\mathrm{I}$ and Part $\mathrm{II}$, containing $5$ and $7$ questions, respectively. A student is required to attempt $8$ questions in all, selecting at least $3$ from each part. In how many ways can a student select the questions?
In an examination, a question paper consists of $12$ questions divided into two parts i.e., Part $\mathrm{I}$ and Part $\mathrm{II}$, containing $5$ and $7$ questions, respectively. A student is required to attempt $8$ questions in all, selecting at least $3$ from each part. In how many ways can a student select the questions?
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
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- [IIT 1994]
If $^{2017}C_0 + ^{2017}C_1 + ^{2017}C_2+......+ ^{2017}C_{1008} = \lambda ^2 (\lambda > 0),$ then remainder when $\lambda $ is divided by $33$ is-
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