The board of directors of a corporation must select a president a secretary and a treasurer in how many possible ways can this be accomplished if there are 22 members on the board of directors

There are 9240 possible ways in which a president, a secretary and a treasurer can be selected from the 22 members on the board of directors.

Solution:

Give that the board of directors of a corporation must select a president a secretary and a treasurer.

Need to calculate in how many possible ways this can be accomplished if there are 22 members on the board of directors

Here we are assuming that one person can hold only one position means one if get selected for president he is out of the race for remaining positions that are secretary and treasure

Lets for sake of understanding, we simplify our question.

Lets say there are 3 members A, B and C. In how many ways two positions of Secretary and treasurer can be filled.

So for selecting secretary we have three option that are A, B or C.

And once secretary is selected, number of option for selecting treasure is two.

So it is found that number of selecting 2 positions for 3 members is product of option available for selecting first position that is secretary multiplied by option available for selecting second position that is treasurer = 3 x 2 = 6

So now applying same logic for selecting members for 3 positions from 22 menbers we get

For selecting president members available = 22

Once president is selected, then option available for selecting a Secretary = 21

And one secretary is also selected, then option available for selecting a treasure = 20

So number of ways in which three positions can be filled by 22 member = 22 x 21 x 20 = 9240

Hence there are 9240 possible ways in which a president, a secretary and a treasurer can be selected from the 22 members on the board of directors.