Question

From a group of 7 newly hired office assistants, 4 are selected. Each of these 4 assistants will be assigned to a different manager. In how many ways can they be selected and assigned? The office assistants can be selected and assigned in different ways.

Answer 1

7 7! 35 There are 7 newly hired assistants & we are making group of 4 . We have to find No. of ways. by.chich_we can make groups of 4. In a single group we cannot repeat any member. &. order of memberin.q-group doesnt matter thence it can be find out by using combination formula C4 41X31 where, 7 is total no. of assistants. 4 is sample size The Groups can be found as below. let us comsider I newly hired asistants are a, b,,d,efig group No Group (a,b,c,d) (b,c,d,e) (c,d,e,f) (, ૨, f ) 1 2 3 4 - 35 (g, a, b,d) Now if any of the group is selected randomly then we are assigning 4 different manggers. to the each newly hired assistant in a group of 4. let P, 9, R us be 4 assistants Then we have to find no. of ways by CS Scanned with CamScanner

There will be a which 4 mana, are assigned to a selected assistants: opory that firstly consider there is I manages to be assigned to I assistant single way to assign (1) Now, consider a different managers to le assigned to a assitants let a, b are assistants & P I are managers then there are a way of assigning a manger to a assistants they are b a b 2!=2. d P g P Now consider 3 different managers (P, 9, R) & 3 assistants (a, b, c) then. a b c C с 9 'a a b c b С. t L g R Р. 9 T ūt P-R ILL U ya P R S 9 P R RP 9 R 4. 5 2 2 31-56 Similarly there are 4 manggers & G assistants then there will be total 29 ways by which. they can be assigned (41 = 24). There are total 35 groups. found them earlier. for each group there are 24 ways to assign a managers thence there will be (35x24) no. of ways to form a a group & assign them to manager as wed g ICS Scanied with 35 X 24 = 840 CamScanner

a b ord AP R g S assio a b cd signed P 9 manager ges bode P Q R S 1 3 c d ef P Q RS a b cd s prg 29 b c de S PRO 2 bĆd d PRIS. (2 ed ef PESS d'ef S PRO (2) (25 (35 gia b d P Q R S ga bd P R O S gaba Group s PR g manager assigned 1 2 24 CS Scanned with CamScanner
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