A book of poetry contains seven poems, three of which are illustrated. In how many different orders can all the poems be read if no two illustrated poems are read one after the other?
Important Questions on Cross-Topic Review Exercise 2
Find the number of ways that seven goats and four sheep can sleep in a row if all the goats must sleep next to each other.
Find the number of ways that seven goats and four sheep can sleep in a row if no two sheep may sleep next to each other.
A teacher is looking for pupils to appear in the school play and has decided to select them at random from a group of girls and boys. Find the number of ways in which the teacher can select the pupils.
A teacher is looking for pupils to appear in the school play and has decided to select them at random from a group of girls and boys.
Two roles in the play must be played by girls; three roles must be played by boys, but the fool can be played by a girl or by a boy. If the first pupil selected is to play the role of the fool, find the probability that the fool is played by a particular girl.
A teacher is looking for pupils to appear in the school play and has decided to select them at random from a group of girls and boys.
Two roles in the play must be played by girls; three roles must be played by boys, but the fool can be played by a girl or by a boy. If the first pupil selected is to play the role of the fool, find the probability that the fool is played by a boy.
A teacher is looking for pupils to appear in the school play and has decided to select them at random from a group of girls and boys.
If instead, the pupil who is to play the fool is the last of the six pupils selected, investigate what effect this change in the order of selection has on the probability that the fool is played by a particular girl.
A teacher is looking for pupils to appear in the school play and has decided to select them at random from a group of girls and boys.
If instead, the pupil who is to play the fool is the last of the six pupils selected, investigate what effect this change in the order of selection has on the probability that the fool is played by a boy.
A radio presenter has enough time at the end of their show to play five songs. She has 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.
