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?

Question

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?

amistre64 · Answer

how many positions are there to fill?

amistre64 · Answer

mmmw  
mmwm
mwmm
wmmm 20.25.24.23.4

20P1 * 25P3 *4C1

mmww  
mwmw
wmmw
mwwm
wmwm
wwmm 20.19.25.24.6

20P2 * 25P2 *4C2

mwww 
wmww
wwmw
wwwm  20.19.18.25.4

25P1 * 20P3 * 4C3

amistre64 · Answer

mwxx 25*20*(24+19)*(24+19-1)
wmxx *2