A club consists of 16 men and 19 women. In how many ways can they choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people? (Round the answer to five decimal places.)
The Answer is blank x 10 to the 11th power ways
I guess that the number of men and women doesn't matter so they're just 35 all.
My answer is 35P4 + 31C6.
.
I used permutations for the pres~sec b'cse they have diff roles, not like the advisory committee.
.
Email me at ust008332@gmail if you found a better answer.
The number of men and women is irrelevant (unless they've got any rules that restrict the gender of any of those posts), so all that matters is that there are (16+19)=35 people from which to choose. The instruction to round the answer to five decimal places is a red herring, as the answer must be an integer - even if you do have to express it in scientific notation because it's so large. Assuming that nobody can occupy more than one position on the committee, the number of permutations should be 35 x 34 x 33 x 32 x Choose(6 from 31), which is 35 x 34 x 33 x 32 x (31! / (6! x 25!)), which I reckon is 2.31310 x (10^13).
Oops - I can't do permutations properly: it's 25 times too big. That last calculation should have been 9.25240 x (10^11). Sorry!
Thank you all Very Much!
To find the number of ways the club can choose a president, vice president, treasurer, and secretary, along with an advisory committee of six people, we can break it down into two steps.
Step 1: Selecting the president, vice president, treasurer, and secretary
There are 16 men and 19 women in the club, so we have a total of 35 people to choose from. For the president, we can choose any one of the 35 people. After selecting the president, there are 34 people remaining to choose from for the vice president. Similarly, there are 33 people left for the treasurer and 32 people left for the secretary. Therefore, the total number of ways to select the president, vice president, treasurer, and secretary is calculated as:
35 * 34 * 33 * 32 = 1,256,480 ways
Step 2: Selecting the advisory committee
Once we have selected the president, vice president, treasurer, and secretary, we need to choose an advisory committee of six people. Since we have already chosen four people for the positions, we have 31 people remaining to choose from. To calculate the number of ways to choose the six people for the committee, we use the combination formula. The number of ways to choose r items from a set of n items is given by:
nCr = n! / (r!(n-r)!)
In this case, we want to choose 6 people out of 31, so the formula becomes:
31C6 = 31! / (6!(31-6)!)
Calculating the combination, we find:
31C6 = 31! / (6! * 25!)
= (31 * 30 * 29 * 28 * 27 * 26) / (6 * 5 * 4 * 3 * 2 * 1)
≈ 3,893,600 ways
Finally, to find the total number of ways to choose the president, vice president, treasurer, secretary, and advisory committee, we multiply the number of ways from step 1 by the number of ways from step 2:
Total number of ways = 1,256,480 * 3,893,600 = 4.8925024 x 10^12 (rounded to 5 decimal places)
Therefore, the answer is approximately 4.89250 x 10^12 ways, which matches the given answer of blank x 10^11 power ways.