Question

In how many ways can 4 individuals be selected from 9 to hold the offices of secretary, treasurer, vice-president, and president, one person per office? a) 30 b) 126 c) 3024 d) 24 e) None of the others The new Senate Ways and Means Committee contains 10 Republicans and 6 Democrats. In how many ways can a subcommittee of 4 be selected, if 3 must be Republicans and 1 must be a Democrat?. a) 126 C(4,3)-C(4,1) b) e) 720 c ) None of the others d) P(4,3)=P(4,1)

Answer 1

Sain - we have totale gindividus For secretary, we have to select one individuals from total g individuals in C(91) ways. for treasurer, we have to select one individual from remaining 8 individuals in C(8.1) ways. for Vice-presidend we have to select one individual from remaining 7 inclividuals in c(7.1) ways. For president .we have to select one individeoul Fung remaining o individuals in CC 6, 1) ways. - Tohal number of ways to select 4 individuals - by selected from a to hold the office of secore secretary treesumed vice aprecident 4 president one person per office. done by a +(91) * C(3.1) xcC1,1) * CC61) ways > 7al ways = c(9,0 X (8,1 x 0(9.1 x <(61) s! ! !!18-1)! (1-13! :(7-D (9-1)! = 9x8x7x6. = 3029 © we have to Republicans 4 6 Domocrats. we have form a subcommittee of a peason. in which В must be republicans 4 I must be 1. Democrats. we have to select 3 Republicans from o in c (10,3) ways 4 seleel | Domocrat from 6 Democrats in C1610 ways: Tofal number of way to Loom a committee of 4 peason with 3 Republicans 4 1 Domo crats a C(103) XC66,1) - Thal ways = c(0,3) XC6)) - the 10-3), * ? th, * 720.