Question

1)A student club has 11 members. How many ways can the club choose a president, vice president, and treasurer?

A.) 330
B.) 990
C.) 165
D.)1,650


2) A student club has 12 members. How many ways can the club choose a president, vice president, secretary, and treasurer?

A.)12,300
B.)6,940
C.)11,880
D.)9,940

Answer 1

In problem 1, there are a total of 11 members and the positions to be elected is only 3. hence to determine the number of ways, we use premutation as the position and order are important. hence 11 P 3 is equal to B. 990 ways.In 2. 12 P 4 is equal to C. 11880 ways

Answer 2

1) The order of selection matters. Therefore we need to find the number of permutations of 11 members taken 3 at a time. 11P3 = 990 ways.
Answer choice B) is correct.

2)The order of selection matters. Therefore we need to find the number of permutations of 12 members taken 4 at a time. 12P4 = 11,880.
Answer choice C) is correct.