Let S 1 = i , j , k : i , j , k ∈ 1 , 2 , … , 10 S 2 = i , j : 1 ≤ i < j + 2 ≤ 10 , i , j ∈ 1 , 2 , … , 10 S 3 = i , j , k , l : 1 ≤ i < j < k < l , i , j , k , l ∈ 1 , 2 , ..... , 10 and S 4 = i , j , k , l : i , j , k and l are distint elements in 1 , 2 , . . . , 10 If the total number of elements in the set S r is n r , r = 1 , 2 , 3 , 4 then which of

Step-by-step solution

S i = i , j , k : i , j , k ∈ 1 , 2 , ... , 10 n 1 = 10 × 10 × 10 = 1000 i.e., number of elements in S 1 = 1000 S 2 = i , j : 1 ≤ i < j + 2 ≤ 10 , i , j ∈ 1 , 2 , ... , 10 j i 1 1 , 2 2 1 , 2 , 3 ⋮ 8 1 , 2 , 3 , . . . . , 9 n 2 = 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 44 S 3 = i , j , k , l : 1 ≤ i < j < k < l , i , j , k , l ∈ 1 , 2 , ....10 n 3 = 10 C 4 = 10 × 3 × 8 × 7 × 6 ! 4 × 3 × 2 × 1 × 6 ! = 210 i.e. number