A club has 5 members from these memebers the positions of president,vice-president,and, treasurer have to be filled how many different ways can these 3 positions be filled
or just P(5,3)
= 5*4*3
= ....
there are 5C3 ways of selecting a group of 3 from 5
there are 3! ways for a group of 3 to fill 3 positions
5C3 * 3! = ?
To find the number of different ways the three positions can be filled (president, vice-president, and treasurer), we can use the concept of permutations. In permutations, the order of selection matters.
Since there are 5 members in the club, there are 5 choices for the first position (president). After selecting the president, there are 4 remaining members to choose from for the vice-president position. Finally, after selecting the president and vice-president, there are 3 remaining members for the treasurer position.
To calculate the number of ways to fill the positions, we multiply the number of choices for each position:
Number of ways = Number of choices for the president * Number of choices for the vice-president * Number of choices for the treasurer
Number of ways = 5 choices for the president * 4 choices for the vice-president * 3 choices for the treasurer
Simplifying the expression, we have:
Number of ways = 5 * 4 * 3 = 60
Therefore, there are 60 different ways the three positions can be filled in the club.