There are 25 men and 20 women who belong to a club. An executive panel consisting of a president, vice president, secretary, and treasurer is being chosen. a) In how many ways cold the executive panel be chosen with NO restrictions? b) In how many ways could the executive panel be chosen if it must include at least one woman and one man? c) In how many ways could the executive panel be chosen if the president and the vice president must have different genders?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given:

men= 25

women = 20

Thus, there are 25 possibilities for vice-president.

So, 20+25–2=43 possibilities for secretary.

as, no person can hold multiple positions, and the secretary can be either male or female.

20x25x43=21500.

Now,

The total number of ways,

=20x25x43 +20x25x43

= 4,043,000.

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