Permutations and Combinations
1 Questions
MSQ (Multiple Correct)
2021
JEE Advanced
MSQ
JEE Advanced 2021 Paper 2 Online
Let
${S_1} = \left\{ {(i,j,k):i,j,k \in \{ 1,2,....,10\} } \right\}$,
${S_2} = \left\{ {(i,j):1 \le i < j + 2 \le 10,i,j \in \{ 1,2,...,10\} } \right\}$,
${S_3} = \left\{ {(i,j,k,l):1 \le i < j < k < l,i,j,k,l \in \{ 1,2,...,10\} } \right\}$ and
${S_4} = \{ (i,j,k,l):i,j,k$ 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?
${S_1} = \left\{ {(i,j,k):i,j,k \in \{ 1,2,....,10\} } \right\}$,
${S_2} = \left\{ {(i,j):1 \le i < j + 2 \le 10,i,j \in \{ 1,2,...,10\} } \right\}$,
${S_3} = \left\{ {(i,j,k,l):1 \le i < j < k < l,i,j,k,l \in \{ 1,2,...,10\} } \right\}$ and
${S_4} = \{ (i,j,k,l):i,j,k$ 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?
A.
n1 = 1000
B.
n2 = 44
C.
n3 = 220
D.
${{{n_4}} \over {12}} = 420$