Question

Please answer this with explanation

A gym has the following group fitness sessions: · Zoomba · Body conditioning · Weight lifting · Boxing · Yoga A member can attend one session at most once a day (i.e., once a member has attended Zoomba classes, s/he cannot attend it again that day). The duration of sessions is also unimportant, however, for example, doing Zoomba before boxing and doing boxing before Yoga should be considered different. We are interested in working out the different ways people can attend the gym sessions.

a) How many different attending (engagement with the fitness sessions) patterns can be formed from those five fitness sessions?

b)How many patterns contain only three types (e.g., yoga – body conditioning - Zoomba)?

c)How many patterns with at least four different activities start with Yoga?

Answer 1

Here there are 5 fitness sessions: Zoomba,body conditioning,weight lifting,boxing,yoga and in the question it mentioned that duration is also unimportant.

a)_ _ _ _ _

There are five empty places and five fitness sessions and a member can attend every fitness session atmost once.By this,it is clear that above 5 empty spaces filled with different fitness sessions.

Explanation:There are five different sessions,so first position can be filled with 5 different ways so first position value is 5.second position value is 4 because a member can attend a session atmost once so 4 sessions are available. now three different sessions available so Third position value is 3.After this 2 different sessions present so second position value is 2.at the end only one different session present so last position value is 1

    5 * 4 * 3 * 2 * 1 =120 patterns

b)_ _ _

Explanation:Three empty positions and five different fitness sessions available.so possibility of first position value is 5.now 4 different sessions and the possibility of second place is 4.one empty position and 3 different sessions,so last position value is 3

5 * 4 * 3 =60 patterns

c) _ _ _ _

Explanation:In the question it is given that pattern starts with yoga.so first empty place is filled with yoga and it is constant.so value is 1.now three empty places and 4 different sessions ,so possibility of second empty space is 4.now two empty places and 3 different sessions so third empty place value is 3.last empty place value is 2 because two different fitness sessions present.

    1 * 4 * 3 * 2 =24 patterns