If $10$ different balls are to be placed in $4$ distinct boxes at random, then the probability that two of these boxes contain exactly $2$ and $3$ balls is 

Out of all possible $8$ digit numbers formed using all the digits $0,0,1,1,2,3,4,4$ a number is randomly selected. Probability that the selected number is odd, is-

It is $5 : 2$ against a husband who is $65$ years old living till he is $85$ and $4 : 3$ against his wife who is now $58$, living till she is $78$. If the probability that atleast one of them will be alive for $20$ years, is $'k'$, then the value of $'49k'$ -

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

All the spades are taken out from a pack of cards.From these cards, cards are drawn one by one without replacement till the ace of spade comes. The probability that the ace of spade comes in the $4^{th}$ draw is

Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively such that $m \le n.\,$ A mapping is selected at random from the set of all mappings from $A$ to $B$. The probability that the mapping selected is an injection is