Five men, four children and two women are asked to stand in a queue at the post office. Find how many ways they can do this if:

the women must be separated

Five men, four children and two women are asked to stand in a queue at the post office. Find how many ways they can do this if:

all of the children must be separated from each other.

Eight-digit mobile phone numbers issued by the Lemon Network all begin with $79.$

How many different phone numbers can the network issue?

Eight-digit mobile phone numbers issued by the Lemon Network all begin with $79.$

Find the probability that a randomly selected number issued by this network:

ends with the digits $97$

Eight-digit mobile phone numbers issued by the Lemon Network all begin with$79.$

Find the probability that a randomly selected number issued by this network:

reads the same left to right as right to left.

The $11$ letters of the word REMEMBRANCE are arranged in a line.

Find the number of different arrangements if there are no restrictions.

The $11$ letters of the word REMEMBRANCE are arranged in a line.

Find the number of different arrangements which start and finish with the letter $M.$