2. Choose one of the *k* *i*=1 *in i * children at random. Show that method...

2. Choose one of the Σ^*k*_*i*=1 *in_i* children at random.

Show that method 1 is more likely than method 2 to result in the choice of a first-born child.

HINT: In solving this problem you will need to show that

$$Σ^*k*_*i*=1 *in_i* Σ^*k*_*j*=1 *n_j* = Σ^*k*_*i*=1 *n_i* Σ^*k*_*j*=1 *n_j*$$

To show the preceding, multiply the sums and show that for all pairs *i*, *j*, the coefficient of the term *n_in_j* is greater in the expression on the left than in the one on the right.