Let S_{1}=\text{{}(i, j, k): i, j, k \in \text{{}1,2, . . ., 10\text{}}\text{}} S_{2}=\text{{}(i, j): 1 \leq i< j+2 \leq 10, i, j \in\text{{}1,2, . . ., 10\text{}}\text{}} S_{3}=\text{{}(i, j, k, l): 1 \leq i< j< k< l, i, j, k, l \in\text{{}1,2, . . ., 10\text{}}\text{}} and S_{4}=\text{{}(i, j, k, l): i, j, k and l are distinct elements in \text{{}1,2, . . ., 10\text{}}\text{}} 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? [JEE Adv 2021 P2]

Permutations and Combinations

Section: Mathematics

Question : 8 of 27

Marks: +1, -0

Let S1={(i,j,k):i,j,k∈{1,2,...,10}}
S2={(i,j):1≤i<j+2≤10,i,j∈{1,2,...,10}}
S3={(i,j,k,l):1≤i<j<k<l,i,j,k,l∈{1,2,...,10}}
and S4={(i,j,k,l):i,j,k and l are distinct elements in {1,2,...,10}}
If the total number of elements in the set Sr is nr,r=1,2,3, 4 , then which of the following statements is (are) TRUE?

[JEE Adv 2021 P2]

n1=1000
n2=44
n3=220
n4
12
=420

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