A shelf'contains 7 Kannada books, 4 Hindi books and 5 English books. In how Example 25. many ways can they be arranged so that (a) The Hindi books are together. (b) Kannada books are together and Hindi books are together. (c) No two English books are together. (d) Books of the same language are together.

How many ways can a baseball line up of 9 players be arrange to hit if the pitcher must bat last, one of the best 4 contact hitters must hit lead-off, and one of two power hitters must bat fourth?

number 10 only

The composer Beethoven wrote 9 symphonies, 5 piano concertos (music for piano and orchestra), and 32 piano sonatas (music for solo plallu). (a) How many ways are there to play first a Beethoven symphony and then a Beethoven piano concerto? ways (b) The manager of a radio station decides that on each successive evening (7 days per week), a Beethoven symphony will be played followed by a Beethoven piano concerto followed by a Beethoven piano sonata. For how many years could this policy be continued before exactly the same program would have to be repeated? (Assume there are 365 days in a year. Round your answer up to the nearest whole number.) years

8. How many ways are there for four men and seven women to stand in a line so that (a) All men stand together and all women stand together? (b) All men stand together? (c) All women stand together? (d) All men stand together or all women stand together?

5.

A grocery store is placing an order for dairy products. There are 8 varieties of dairy products sold in cases, where each case contains all the same variety of dairy products. The store will order 50 cases in total. (a) How many ways are there to place the order? (b) One of the varieties of dairy products is Milk. How many ways are there to place the order if they order at most 20 cases of Milk?

How many strings of ten English letters are there that start with AB and end with Y Z and contain at least one vowel if letters can be repeated ?How many ways are there for 8 men and 5 women to stand in a line so that no two women stand next to each other ?How many ways are there for 5 men and 7 women to stand in a line so that all women stand

Suppose there are 5 men and 8 women qualified to be members of a new committee of 6 people, includinga president, a vice-president, and a secretary.(a) How many different ways do you have to pick a president, vice-president and secretary if you need atleast 1 men and 1 women? Does the order matter? Why?(b) How many different committees can you form with at least 3 women? Does the order matter? Why?

A baseball fan purchases 6 red “Home Game” shirts and 10 blue “Away Game” shirts. For part (b), assume all the shirts are identical except for their color (b) How many ways are there to hang all of the shirts on the clothesline if we don’t want 2 red shirtsnext to each other?