Answer to Question #189376 in Discrete Mathematics for Muhamad awais

Question

There are 18 325 Computer and 415 English majors at colege . ( a ) How many ways to pick 5 math 125 computer and 300 English majors ? many ways to pick one Yepresenta tative who is either Math or computer . Eng / i * s * h ? ( 6 ) How

Answer 1

Given,

Mathematics major = 18

Computer majors = 325

English majors = 415

So,

Number of ways to select 5 Math majors out of 18 majors = $^{18}C_5$

Number of ways to select 125 Computer majors out of 325 majors = $^{325}C_{125}$

Number of ways to select 300 English majors out of 415 majors = $^{415}C_{300}$

(a) Using product rule because the first event is picking a Mathematics major and second event is picking Computer major and third event is picking English major

$$^{18}C_{5}\times^{325}C_{125}\times ^{415}C_{300}$$

(b) Using sum rule because the first event is picking a Mathematics major OR second event is picking Computer major OR third event is picking English major

$$^{18}C_{5}+^{325}C_{125}+ ^{415}C_{300}$$