Question

A pharmaceutical company is to select a new board ofdirectors. Each member on the board will have an equalvoice. There are 15 people to choose from, however thereis only room for 5 members on the board. How manydifferent boards could be formed from the 15 people?PermuatationCombination

Answer 1

If we take a look, we could say that

For the first selected new board member, we have 15 options

for the second one, we have 14 options (because one of the persons was already chosen)

for the third one we have 13 option, 4th one 12 options and 5th one 11 options

So to get the number of different boards we need to multiply the options for each one, so:

15*14*13*12*11= 360360

now we need to divide for the number of member of the board that need to be chosen so

5*4*3*2*1

So the different boards are:

`(15\cdot14\cdot13\cdot12\cdot11)/(5\cdot4\cdot3\cdot2\cdot1)=3003`

3003 different boards could be formed