Dean Chalmers and Julian Gilbey Solutions for Chapter: Cross-Topic Review Exercise 2, Exercise 1: CROSS-TOPIC REVIEW EXERCISE 2

A radio presenter has enough time at the end of their show to play five songs. She has $13$ songs by four groups to choose from: five songs by The Anvils, four by The Braziers, three by The Chisels and one by The Dustbins. Find the number of ways she can choose five songs to play if she decides that there should be no restrictions.

A radio presenter has enough time at the end of their show to play five songs. She has $13$ songs by four groups to choose from: five songs by The Anvils, four by The Braziers, three by The Chisels and one by The Dustbins. Find the number of ways she can choose five songs to play if she decides to play all three songs by The Chisels.

A radio presenter has enough time at the end of their show to play five songs. She has $13$ songs by four groups to choose from: five songs by The Anvils, four by The Braziers, three by The Chisels and one by The Dustbins. Find the number of ways she can choose five songs to play if she decides to play at least one song by each of the four groups.

Students enrolling at an A Level college must select three different subjects to study from the six that are available. One subject must be chosen from each of the option groups $A, B,$ and $C,$ as shown in the following table.

Students enrolling at an A Level college must select three different subjects to study from the six that are available. One subject must be chosen from each of the option groups $A, B,$ and $C,$ as shown in the following table.

Four ordinary fair dice are arranged in a row. Find the number of ways in which this can be done if the four numbers showing on top of the dice are all odd.

Four ordinary fair dice are arranged in a row. Find the number of ways in which this can be done if the four numbers showing on top of the dice have a sum that is less than $7.$

A conference hall has $24$ overhead lights. Pairs of lights are operated by switches next to the main entrance, and each switch has three numbered settings: $0$(off), $1\left(dim\right), 2$ (bright). Find the number of possible lighting arrangements in the hall if three lights that are not operated by the same switch and five pairs of lights that are operated by the same switch are not working.