Let S1= ( i , j , k ): i , j , k ∈ 1,2, ldots ., 10 S2= ( i , j ): 1 ≤ i

Question

Let S1= ( i , j , k ): i , j , k ∈ 1,2, ldots ., 10 S2= ( i , j ): 1 ≤ i < j +2 ≤ 10, i , j ∈ 1,2, ldots . .10 S3= ( i , j , k , l ): 1 ≤ i < j < k < l , i , j , k , l ∈ 1,2, ldots ., 10 and S4= ( i , j , k , l ): i , j , k and l are distinct elements in 1,2, ldots ., 10 If the total number of elements in the set S r is n r , r =1,2,3,4, then which of the following statements is(are) TRUE? (A) n1=1000 (B) n2=44 (C) n3=220 (D) ( n 4/12)=420

Tardigrade Admin · Accepted Answer

n 1=10 × 10 × 10=103 n 2= 8 C 2+2 8 C 1=44 n 3= 10 C 4=210 n 4= 10 P 4=5040

$n_{1} = 1000$

$n_{2} = 44$

$n_{3} = 220$

$\frac{n _{4}}{12} = 420$

$n_{1} = 10 \times 10 \times 10 = 1 0^{3}$
$n_{2} =^{8} C_{2} + 2^{8} C_{1} = 44$
$n_{3} =^{10} C_{4} = 210$
$n_{4} =^{10} P_{4} = 5040$

n1​=1000

n2​=44

n3​=220

12n4​​=420

n1​=10×10×10=103 n2​=8C2​+28C1​=44 n3​=10C4​=210 n4​=10P4​=5040

$n_{1} = 1000$

$n_{2} = 44$

$n_{3} = 220$

$\frac{n _{4}}{12} = 420$

$n_{1} = 10 \times 10 \times 10 = 1 0^{3}$
$n_{2} =^{8} C_{2} + 2^{8} C_{1} = 44$
$n_{3} =^{10} C_{4} = 210$
$n_{4} =^{10} P_{4} = 5040$