n₁ = number of elements in S₁ = 10 $$\times$$ 10 $$\times$$ 10 = 1000

n₂ = number of elements in S₂ = 8 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

= 8 + $${{8 \times 9} \over 2} = 44$$ ($$\because$$ 1 $$\le$$ i < j + 2 $$\le$$ 10 $$\Rightarrow$$ j $$\le$$ 8 and i $$\ge$$ 1

$$\therefore$$ (i = 1, j = 1, 2, 3, .... 8), (i = 2, j = 1, 2, 3, ..... 8), (i = 3, j = 2, 3, 4, .... 8) and so on)

n₃ = number of elements in S₃ = $${}^{10}{C_4}$$

(selecting 4 numbers and arranging in increasing order)

$$ = {{10 \times 9 \times 8 \times 7} \over {24}} = 210$$

n₄ = number of elements in S₄ = $${}^{10}{C_4}$$ = 10 $$\times$$ 9 $$\times$$ 8 $$\times$$ 7

$$ \Rightarrow {{{n_4}} \over {12}} = 420$$