I have $5$ different physics textbooks and $4$ different chemistry textbooks. In how many ways can I place the $9$ textbooks on a bookshelf, in a row, if there must be a chemistry textbook in the middle, and there must be a physics textbook at each end

57600

Explanation:

Given the following;

5 different physics textbooks

4 different chemistry textbooks

There are 9 different positions for arranging the textbooks on a shelf.

If there must be a physics textbook at both ends;

Number of physics textbooks = 5

Both ends = 2 different positions

Mathematically,

5P2 = 5! ÷ (5-2)!

5! ÷ 3!2! =(5×4)

5P2 = 20 ways

If a chemistry textbook must be in the middle;

Number of chemistry textbooks = 4

Middle = 1 position

Mathematically,

4P1 = 4! ÷ (4-1)!

4P1 = 4! ÷ 3!

4P1 = 4 ways

3 positions have been calculated,

The 6 positions left = 6!

6! = 720ways

Therefore,

6! × 5P2 × 4P1 = 720 × 20 × 4 = 57600

2 weeks ago lol enoy your dunce cap

someone i feel is a leader in my life id have to say would be my mother because she has give me great advice in life and got me out of tough situations. some characteristics she has are creativity, honesty, commitment, respect for others, and communication. one example of a situation when she demonstrated leadership was when i was working late on homework and i started to get stressed and got upset, she asked me if i needed some , and she me with my work. she demonstrated communication and commitment.

i don't know if this is exactly what your looking for but i hope this !