In how many ways can $35$ apples be distributed among $3$ boys such that each boy can have any number of apples?

If $^{10}C_r = ^{10}C_{r+2}$,then $^5C_r$ equals

The number of $4$-digit numbers without repetition that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ in which each number has two odd digits and two even digits is:

$A$ box contains $2$ white balls,$3$ black balls,and $4$ 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?

$A$ team of $11$ players is to be selected from $22$ players. If $2$ specific players must be included in every team and $4$ specific players must always be excluded,in how many ways can this selection be made?

$A$ student has to answer a multiple-choice question having $5$ alternatives in which two or more than two alternatives are correct. Then the number of ways in which the student can answer that question is