Question

A teacher has four books A, B, C, and D to assign to four students in any order he prefers. Set S includes all possible arrangements of the four books. Set X includes all possible arrangements. If book C is chosen first and D is chosen second, in how many ways can the teacher assign the books?

A) 24 ways
B) 2 ways
C) 6 ways
D) 4 ways

Answer 1

When book C is assigned first and D second, there are 2! permutations for the remaining two books, giving us 2 ways to assign the remaining books A and B.

Step-by-step explanation:

The subject question pertains to permutations and combinations, which is part of Mathematics. Given that the teacher needs to assign books A, B, C, and D, with C always assigned first and D second, we need to calculate how many arrangements of books A and B are possible in the remaining two positions.

Since the first two positions are fixed (C and D), there are two positions left to fill. There are 2 books to choose from for the third position and 1 book for the final position. Hence, the number of permutations is calculated as 2! (two factorial), which equals 2 x 1 = 2 ways.

The answer to the question of how many ways the teacher can assign the books if book C is chosen first and D is chosen second is thus B) 2 ways.