Since all books of the same branch must be together, put the 3 different branches into 3 SEPARATE BLOCKS, as follows:Joy Shaha wrote:Q. In how many different ways can 4 MATH, 3 ENGLISH & 2 ANALYTICAL ABILITY books arranged in a row so that all books of the same branch are together?
A.864;
B.1484;
C.1726;
D.1728;
E.1734
Let the math block = [ABCD]
Let the English block = [RST]
Let the analytical block = [XY].
Number of ways to arrange the 3 blocks [ABCD], [RST] and [XYZ] = 3!.
Within the math block, the number of ways to arrange books A, B, C and D = 4!.
Within the English block, the number of ways to arrange books R, S and T = 3!.
Within the analytical block, the number of ways to arrange books X and Y = 2!.
To combine the options above, we multiply:
3!4!3!2! = 6*24*6*2.
The product of the units digits = 6*4*6*2 = 24*12 = integer with a units digit of 8.
Thus, the correct answer choice must have a units digit of 8.
The correct answer is D.
