How many words,with or without meaning,each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?

Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also,find the number of elements of this sample space.

While dialing a telephone number,an old man forgets the last two digits,remembering only that these are different. If he dials the last two digits at random,what is the probability that the number is dialed correctly?

Eight chairs are numbered $1$ to $8$. Two women and three men wish to occupy one chair each. First,the women choose the chairs from amongst the chairs marked $1$ to $4$,and then the men select the chairs from amongst the remaining. The number of possible arrangements is

How many words,with or without meaning,each of $2$ vowels and $3$ consonants can be formed from the letters of the word $DAUGHTER$?

If ${ }^{22} P_{r+1}:{ }^{20} P_{r+2}=11: 52$,then $r=$