A 3-member executive committee is to be formed from a 11-member board of directors. In how many ways can it be formed?
6
170
165
33
990
Please explain this to me. thank you
11*10*9 = 990
or
11!/(11-3)! = 11!/8!
In the majority of texts the word "committee" usually denotes combinations, that is there is no specific order.
In that case the result would be C(11,3) which is 165
But you titled your post "permutations", so Steve's answer would apply for that interpretation.
Choose your answer after you clear up the wording of the question.
Well, let's calculate it the funny way!
So, you have an 11-member board of directors and you need to form a 3-member executive committee. It's like trying to pick your favorite ice cream flavors from a delicious ice cream parlor!
To solve this, we use a combination formula, which is like using a scoop to pick the flavors of your committee. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices you need to make.
So, for your case, we have 11 directors to choose from and we need to form a committee with 3 members. Putting it into the formula, we have 11C3 = 11! / (3!(11-3)!).
Now, let me do some quick math here. 11! is like trying to count the number of sprinkles on a gigantic sundae, and it equals 39,916,800. Woah!
But wait, there's more! We need to divide that by the product of 3! and (11-3)!. 3! is 3 x 2 x 1, which is 6, and (11-3)! is the same as 8!, which is 40,320. Are you following?
Now, let's do the final calculation. 39,916,800 divided by (6 x 40,320). And the answer is... drumroll, please... 165!
So, it looks like the answer is 165 ways to form the executive committee. You have 165 different combinations of three members that you can pick from your board of directors ice cream parlor. Have fun scooping out your committee!
To determine the number of ways a 3-member executive committee can be formed from an 11-member board of directors, we can use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where "n" represents the total number of options, and "r" represents the number of choices we want to make.
In this case, we want to choose a 3-member executive committee from a 11-member board of directors. Thus, we have n = 11 and r = 3.
Using the formula, we can calculate the value of C(11, 3) as follows:
C(11, 3) = 11! / (3!(11-3)!)
= 11! / (3! * 8!)
= (11 * 10 * 9 * 8!) / (3! * 8!)
= (11 * 10 * 9) / (3 * 2 * 1)
= 165
Therefore, the number of ways the 3-member executive committee can be formed is 165. Hence, the correct answer is option C.
To find the number of ways a 3-member executive committee can be formed from an 11-member board of directors, we can use the concept of combinations.
The formula to find the number of combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of items, and r is the number of items we want to select.
In this case, we want to select a 3-member executive committee from a pool of 11 board members. So, n = 11 and r = 3.
Plugging these values into the formula, we get:
11C3 = 11! / (3!(11-3)!)
= 11! / (3!8!)
Now, let's calculate the factorial values:
11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
3! = 3 × 2 × 1
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Simplifying the equation further, we get:
11C3 = (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / [(3 × 2 × 1) × (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)]
= (11 × 10 × 9) / (3 × 2 × 1)
= 990 / 6
= 165
Therefore, the number of ways a 3-member executive committee can be formed from an 11-member board of directors is 165. Hence, the answer is option C) 165.