Carcass wrote:
In how many different ways can 10 students of a class with roll numbers from 1 to 10 be seated in a straight line such that one of the extreme positions has a student with an odd roll number while the other extreme position has a student with an even roll number?
(A) 48 × 6!
(B) 44 × 12!
(C) 50 × 8!
(D) 50 × 6!
(E) 52 × 8!
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GRE Tips and Tricks - UPDATED 11/20/2021There are two possible cases:
case i: ODD _ _ _ _ _ _ _ _ EVEN5 options for 1st position
5 options for 10th position
8 options for 2nd position
7 options for 3rd position
6 options for 4th position
.
.
.
2 options for 8th position
1 option for 9th position
TOTAL = (5)(5)(8)(7)(6)....(3)(2)(1)
=
(25)(8!)case ii: EVEN _ _ _ _ _ _ _ _ ODD5 options for 1st position
5 options for 10th position
8 options for 2nd position
7 options for 3rd position
6 options for 4th position
.
.
.
2 options for 8th position
1 option for 9th position
TOTAL = (5)(5)(8)(7)(6)....(3)(2)(1)
=
(25)(8!)GRAND TOTAL =
(25)(8!) +
(25)(8!) =
(50)(8!)Answer: C