An academic department has just completed voting by secret ballot for a department head. The ballot box contains four slips with votes for candidate ?A ?and three slips with votes for candidate ?B. ?Suppose these slips are removed from the box one by one. a?? ist all possible outcomes. b?. ?Suppose a running tally is kept as slips are removed. For what outcomes does ?A remain ahead of B? ?throughout the tally?

Answer : Step 1 of 2 : Given, An academic department has just completed voting by secret ballot for a department head. The ballot box contains four slips with votes for candidate A and three slips with votes for candidate B a) The claim is to the all possible outcomes So, we have 4 A and 3 B slips. Totally 7 slips in a box If the slips are removed from the box one by one, then the outcomes are ( BBBAAAA, BBABAA, BBAABAA, BBAAABA, BBAAAAB, BABBAAA, BABABAA, BABAABA, BABAAAB, BAABBAA, BAABABA, BAABAAB, BAAABBA, BAAABAB, BAAAABB, ABBBAAA, ABBABAA, ABBAABA, ABBAAAB, ABABBAA, ABABABA, ABABAAB, ABAABBA, ABAABAB, ABAAABB, AABBBAA, AABBABA, AABBAAB, AABABBA, AABABAB, AABAABB, AAABBBA, AAABBAB, AAABABB, AAAABBB) There are 35 possible outcomes.