The number of ways in which $5$ beads of different colours form a necklace is

The number of four-letter words that can be formed using the letters of the word $BARRACK$ is

In a touring cricket team,there are $16$ players in all,including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players can be chosen from these,such that each team includes exactly $3$ bowlers and $1$ wicket-keeper?

How many numbers lying between $1000$ and $10000$ can be formed by using the digits $1, 3, 5, 6, 7, 8, 9$ if no digits are repeated?

How many different numbers of $6$ digits can be formed with the digits $3, 1, 7, 0, 9, 5$?

How many groups can be selected for playing football out of $5$ ladies and $4$ gentlemen such that there should be one lady and one gentleman on each side?