1. In how many ways can a committee of 5 be formed from 5 juniors and 7 seniors if the committee must have 3 seniors?
We need to select a committee of 5 from 5 juniors and 7 seniors.
Now 3 of seniors are to be selected.
So, that we need 2 members from total of 5
2 members from total of 5juniors and 4 seniors.
Case 1
Where both are juniors
So, we need 5 C 2 i.e. 10 cases
Case 2
Where 1 is junior and other is senior
So we need 5 C1 +4 C 1 i.e. 9
Case 3
Where both are seniors
Here we need 4 C 2 i.e. 6
So total cases
=10+9+6
=25 are the total cases
2. From a population of 50 households, in how many ways can a researcher select a sample with a size of 10?
50C10
= 50! / (50-10)! * 10! = (50 * 49…* 41) / (1 * 2…* 10) = 1.02723 x 10^18 ways
3. A box contains 5 red balls, 7 green balls, and 6 yellow balls. In how many ways can 6 balls be chosen if there should be 2 balls of each color?
There are 5C2 = 10 ways of getting 2 reds
There are 7C2 = 21 ways of getting 2 greens
There are 6C2 = 15 ways of getting 2 yellows
Hence, there are 10*21*15= 3150 ways of picking 6 balls under this restriction
Hence, there are 10*21*15= 3150 ways of picking 6 balls under this restrictionIf there were no restrictions then there would be 18C6 = 18564 ways of picking 6 balls.
4. From 7 Biology books and 6 Chemistry books, in how many ways can one select 2 Biology and 2 Chemistry books to buy if all the said books are equally necessary?
we have to choose 2 from each subject separately and multiply the answer to get all combinations.
=( Choose 2 from 7)*(choose 2 from 6)
=7C2 *6C2
=21*15
=315
5. Mrs. Riveras business is gown rental and sale. She decided one day that she would display her 10 newest gowns in her shops window to attract customers. If she only had 5 mannequins and planned to change the set of gowns every 2 days. how many days will have to pass before she runs out of a new set to display?
4 days
Days:
2 = and it is the day rhat she wants to change the mannequins to five new set of gowns; after
2 = days it is the day that shes going to change the last five new set of gowns.
The Answer without solution is...
1. 25
2. 50C10
3. 18C6
4. 315
5. 4
Hope it helps also pabrainlest ty ^•^