if there are 6 candidates in an election and voters are asked to rank all of the candidates how many different pairwise comparisons are there

A committee consists of five executives, three women and two men. Their names are Maria (M),John (J), Susan (S), Will (W) and Holly (H). The committee needs to select a chairperson and a secretary. Itdecides to make the selection randomly by drawing straws. The person getting the longest straw will beappointed chairperson, and the one getting the shortest straw will be appointed as secretary. The possibleoutcomes can be represented in the following manner.MS SM HM JM WM MH SH HS JS WSMJ SJ HJ JH WH MW SW HW JW WJHere, for example, MS represents the outcome that Maria is appointed chairperson and Susan is appointed assecretary.(a)  List the outcomes constitution each of the following four eventsA = Event a male is appointed chairpersonB = Event Holly is appointed chairpersonC = Event Will is appointed secretaryD = Event only females are appointed(b)  Calculate P(not A)(c)  Calculate P(B and D)(d)  Calculate P(B or C)   (maria,susan and holly are female/women and john and will are male)

In order to conduct an​ experiment, 5 subjects are randomly selected from a group of 50 subjects. How many different groups of 5 subjects are​ possible?   the number of possible different groups is

Suppose you are interviewing 25 people in order to fill 5 job vacancies. How many possible choices of 5 people are there to fill those vacancies?