3 Word Problems

[nvr_hom]

How would I go about solving these problems. Show me the steps please..

4.
Your small library of books consists of 5 novels, 4 mathematics books, and 1 biology book. Calculate the number of ways to arrange them on a bookshelf for each of these situations.

The mathematics books must be together and the novels must be together?


7.
How many 5-digit bank security Personal Identification Numbers (PIN) codes can be formed using the characters in the set {0, 2, 4, 6, 8, a, b, c, d, y } with the restrictions below.

Note: For purposes of this problem, the PIN number can be "padded" with zeros on the left. So a 0z01a is a good PIN. (IE, PIN codes can start with zeros.)

PINs must use exactly three a's among the five characters. (with replacement)



8.
A department contains 10 men and 20 women.

How many ways are there to form a committee with 6 members if it must have strictly more women than men?

(Points : 1)

 

[galactus]

How would I go about solving these problems. Show me the steps please..

4.
Your small library of books consists of 5 novels, 4 mathematics books, and 1 biology book. Calculate the number of ways to arrange them on a bookshelf for each of these situations.

The mathematics books must be together and the novels must be together?

This depends. Are the books all different?. For example, are the math books considered different or all the same?

If they are the same, then lump the math books together, the novels together. There is only one bio book, so there are only 3! arrangements.

If they are different, that is another matter. I hate when problems are not specific.

7.
How many 5-digit bank security Personal Identification Numbers (PIN) codes can be formed using the characters in the set {0, 2, 4, 6, 8, a, b, c, d, y } with the restrictions below.

Note: For purposes of this problem, the PIN number can be "padded" with zeros on the left. So a 0z01a is a good PIN. (IE, PIN codes can start with zeros.)

PINs must use exactly three a's among the five characters. (with replacement)

How many ways can you place 3 a's in 5 places?. Then, think about filling the other two positions. There are 9 choices of digits and letters to choose from with repetition allowed.

8. A department contains 10 men and 20 women.

How many ways are there to form a committee with 6 members if it must have strictly more women than men?

If there are more women than men, then there can be 4 women and 2 men, 5 women and 1 man, or 6 women and no men.

Find the number of ways for each scenario and add them up.