The Teknomite Corporation must appoint a president, chief executive officer (CEO), a chief operating officer (COO). It must also appoint a planning Committee with three different members. There are eight qualified candidates, and officers can also serve on the committee. How many ways can the officers be appointed? How many different ways can the committee be appointed?

336 ways ;

56 ways

Step-by-step explanation:

Number of ways to have the officers :

Number of qualified candidates, n = 8

Number of officer positions to be filled = 3

A.)

Using permutation (since the ordering matters):

nPr = n! ÷(n-r)!

8P3 = 8! ÷ (8-3)!

8P3 = 8! ÷ 5!

8P3 = (8*7*6)

8P3 = 336 ways

B.) Different ways of appointing committee: (ordering doesn't count as officers can also be appointed)

Using the combination relation :

nPr = n! ÷(n-r)!r!

8C3 = 8! ÷ (8-3)! 3!

8C3 = 8! ÷ 5!3!

8C3 = (8*7*6) ÷ (3*2*1)

8C3 = 336 / 6

8C3 = 56 ways

b

step-by-step explanation:

ez

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18