An urn contains 4 blue balls and 6 orange balls. in how many ways can we select 2 blue balls and 5 orange balls from the urn? a) 24 b) 38 c) 36 d) 732 e) 8637 f) none of the above.

b) 36

Step-by-step explanation:

We can use combinations to solve this problem.

The binomial coefficient counts the number of ways of choose k elements from a set of n elements.

The product rule from combinatorics says that if there are N ways of doing something and M ways of doing another thing, the number of ways of doing both things is equal to NM.

First, we choose the blue balls. The urn contains 4 blue balls and we select 2 so there are ways of doing this. Similarly, we choose the 5 orange balls from the set of 6 in the urn, which can be done in ways. By the product rule, there are MN=6(6)=36 ways of selecting all the balls.

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

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