We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?

Asked by shaktidevgun | 26th Sep, 2015, 08:05: PM

Expert Answer:

begin mathsize 16px style Formula colon nC subscript straight r equals fraction numerator straight n factorial over denominator straight r factorial open parentheses straight n minus straight r close parentheses factorial end fraction The space 6 space pesons comma out space of space 8 space can space be space chosen space in space th r ee space ways comma as space per space the space given space condition comma space space open parentheses If space the space person space straight A space is space chosen comma space then space straight B space must space be space chosen comma space but space person space straight B space can space be space chosen space without space person space straight A close parentheses Case space 1 colon space straight A space and space straight B space both space are space not space included space This space can space be space done space in space 6 straight C subscript 6 equals 1 space way Case space 2 colon space straight A space and space straight B space both space are space included space This space can space be space done space in space 1 cross times 1 cross times space space 6 straight C subscript 4 equals fraction numerator 6 factorial over denominator 4 factorial open parentheses 6 minus 4 close parentheses factorial end fraction equals fraction numerator 6 factorial over denominator 4 factorial cross times 2 factorial end fraction equals 15 Case space 3 colon space straight B space is space included space but space straight A space is space not space included space This space can space be space done space in space 1 cross times space space 6 straight C subscript 5 equals fraction numerator 6 factorial over denominator 5 factorial open parentheses 6 minus 4 close parentheses factorial end fraction equals fraction numerator 6 factorial over denominator 5 factorial end fraction equals 6 Hence space total space number space of space ways space are space 1 plus 15 plus 6 equals 22 end style

Answered by Priti Shah | 28th Sep, 2015, 11:07: AM