no. of ways of selecting p & q from {1,2,3,.....,9,10} so that |p-q|<4

Consider p<q and

Case I: q-p=3

For p=1,2,3,...,6,7  no. of values of q satisfying resp. values are in order, 7,6,5,,...,2,1.

Thus for p<q there are 21 options.

Now as |p-q|=3, we have other 21 pairs. In all, 42 for |p-q|=3.

Case II : diff.=2

There are 28+28=56 pairs as done by method in case I.

Case II : diff.=1

There are 36+36=72 pairs as done by method in case I.

Thus in all, no. of ways = 72+56+42 = 172.