Let $A = \{(a, b, c) : a, b, c \text{ are non-negative integers and } a + b + 2c = 22\}$. Then $n(A)$ is equal to:

$A$ question paper has $3$ parts $A, B, C$. Part $A$ contains $7$ questions,part $B$ contains $5$ questions,and part $C$ contains $3$ questions. If a candidate is allowed to answer not more than $4$ questions from part $A$,not more than $3$ questions from part $B$,and not more than $2$ questions from part $C$,then the number of ways in which a candidate can answer exactly $7$ questions is

If $^n{P_4} = 30 \times {^n}{C_5}$,then $n = $

Five-digit numbers are formed using the digits $1, 2, 3, 5, 7$ with repetitions and are written in descending order with serial numbers. For example,the number $77777$ has serial number $1$. Then the serial number of $35337$ is $.........$.

Out of $7$ consonants and $4$ vowels,words are formed each having $3$ consonants and $2$ vowels. The number of such words that can be formed is

The number of $3$-digit odd numbers divisible by $3$ that can be formed using the digits $1, 2, 3, 4, 5, 6$ when repetition is not allowed is: