There are seven seats in each row of a classroom. luke and lester are assigned to after-school detention and they must sit in the front row of the classroom, but they cannot sit next to each other because they might talk. how many ways can these two students be seated in the row?

480 Ways

Explanation:

Let z represent they must not sit together

z = (7-1) factorial ways

z = 6 factorial ways

Let x = the no. of ways the two children can be seated in 7 seats without seating next to each other

x = 2*5 factorial ways

Let y = no of ways the children can be seated on 7 seats, if the must not seat next to each other

z = x + y

y = z -x

y = 6 factorial minus 2*5 factorial

y = 6*5 factorial minus 2*5 factorial

y = 5 factorial (6-2)

y = 5 factorial times 4

y = 5*4*3*2*1*4

y = 480 ways.

The Battle of Midway

From June 4-7 in 1942, the United States Navy decisively turned the tide of the War in the Pacific with its victory at the Battle of Midway.

Led by Admirals Nimitz, Fletcher, and Spruance, the Battle hinged on a surprise air attack and the resulting damage to the Japanese Navy proved to be so damaging that they struggled to recover from the loss.