Answer:
Please see the answer below
Step-by-step explanation:
a. Since there’s no restrictions .Therefore , the number of ways = 7!*150 = 756000
b. The number of ways such that the 4 math books remain together
The pattern is as follows: MMMMEEE, EMMMMEE, EEMMMME, and EEEMMMM
Where M = Math’s Book and E= English Book.
Number of ways = 4!*8!*4*150= 86400 ways.
c. The number of ways such that math book is at the beginning of the shelf
The number of ways = 6!*4*150 = 432000
d. The number of ways such that math and English books alternate
The number of ways = 150*4!*3! =2160 ways
e. The number of ways such that math is at the beginning and an English book is in the middle of the shelf. The number of ways = 4*3*5!*150 =216000 ways.
