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10.4.3: lining up club members for a photo. help outline ten members of a club are lining up in a row for a photograph. the club has one president, one vp, one secretary, and one treasurer. (a) how many ways are there to line up the ten people? (b) how many ways are there to line up the ten people if the vp must be beside the president in the photo? (c) how many ways are there to line up the ten people if the president must be next to the secretary and the vp must be next to the treasurer?



Answer :

tutorconsortium270

A)  number of ways in which president is not next to the VP =3628800-725760 =2903040

B) Number of ways =9*9!=3265920

C) number of ways VP is in one end  =2*9!=725760

What is permutation and combination ?

Permutations and combinations are  ways of representing groups of objects by selecting them  and sub-setting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.

Calculation

a)

number of ways to line up 10 members =10! =3628800

number of ways so that VP and president are next to each other =N(consider president and VP as 1 member which can interchange in 2 ways , and now we need to arrange 9 members) =2*9!=725760

therefore number of ways in whcih president is not next to the VP =3628800-725760 =2903040

b)

Number of ways =N(9 choices for left most posiition except VP and arrange rest of 9 persons)

=9*9!=3265920

c)

number of ways VP is in one end =N(choose 1 place out of 2 end for VP and then arrange rest of 9 )

=2*9!=725760

therefore number of ways VP is not at one end =3628800-725760 =2903040

learn more about permutations and combinations here :

brainly.com/question/28720645

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