The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is

$A$ library has $a$ copies of one book,$b$ copies of each of two books,$c$ copies of each of three books,and single copies of $d$ books. The total number of ways in which these books can be arranged is

In a certain test,${a_i}$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, 3, ..., k$. No student gave more than $k$ wrong answers. The total number of wrong answers given is:

$A$ question paper is divided into two parts $A$ and $B$,and each part contains $5$ questions. The number of ways in which a candidate can answer $6$ questions by selecting at least two questions from each part is:

Out of $10$ white,$9$ black and $7$ red balls,the number of ways in which selection of one or more balls can be made,is

All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is