If 4. 6p_r = 6 p_r + 1, then r is equal to ________.

The number of lines drawn through 6 points lying on a circle is ______

Twelve students compete for a race.  The number of ways in which first three places can be taken as ______.

The number of handshakes that can be exchanged among a party of 12 students if every student strikes hands once with every other  student is _________.

If ⁿc₂ = ⁿc₃ , then the value of ⁿc₄ is ________.

The number of ways in which 21 objects can be grouped into three groups 8,7 and 6 objects is _____

There are four letter boxes in a post office.  In how many ways can a man post  8 distinct letters.

In an examination, a student has to answer 4 questons out of 6. questions 1 and 2 are however, compulsary.  The number  of ways in which the students can make the choice is _______.

Six identical coins are arranged in a row.  The  number of ways in which the  number of tails is equal to number of heads is _______.

The number of ways in which 5 boys and 5 girls can sit in a row so that all the girls sit together is ______.