1. A lottery game requires that you pick 7 different numbers from 1 to 51. If you pick all 7 winningnumbers, you win the jackpot. If you pick 6 of the 7 numberscorrectly, you win $300,000. In how many ways can you pick exactly 6 of the 7 winning numbers without regard toorder?

There are ________ways to pick exactly 6 of the 7 winning numbers without regard to order.

2. A lottery game requires that you pick 5 different numbers from 1 to 63. If you pick all 5 winningnumbers, you win the jackpot. Complete parts(a) and(b) below.

How many ways are there to choose 5 numbers if order is notimportant? Choose the correct answer below.

A.

There are 502,452,720 ways to choose the numbers.

B.

There are 7,028,847 ways to choose the numbers.

C.

There are 843,461,640 ways to choose the numbers.

D.

There are 120 ways to choose the numbers.

3. six orchids from a collection of 24 are to be selected for a flower show. Complete parts(a) and(b) below.

(a) In how many ways can this bedone?

This can be done in_______ways.

4. A legislative committee consists of 10 Democrats and 4 Republicans. A delegation of 4 is to be selected to visit a small island republic. Complete parts(a) through(d) below.

(a) How many different delegations arepossible?

The 4 delegates can be selected_______ different ways.

5. A group of 8 workers decides to send a delegation of 4 to their supervisor to discuss their grievances. Complete parts(a) through(c) below.

(a) How many delegations arepossible?

There are _______ delegations possible.

6. From a group of 10 newly hired officeassistants, 3 are selected. Each of these 3 assistants will be assigned to a different manager. In how many ways can they be selected andassigned?

The office assistants can be selected and assigned in______ different ways.

7. Nine cards are marked with the numbers 1,2,3,4,5,6,7,8,and9, thenshuffled, and three cards are drawn.

a. How many different 3-card combinations arepossible?

b. How many 3-card hands contain a number less than four?

8. A game uses a special deck of cards. Each card has eitherone, two, or three identicalshapes, all of the same color and style. There are three possibleshapes: squiggle, diamond, andoval. There are five possiblecolors: green,purple,red,yellow,andblack. There are four possiblestyles: solid,shaded,outlined,ordotted. The deck consists of all possible combinations ofshape, color,style, and number of shapes. How many cards are in thedeck?

There are _____ cards in the deck.

9. A concert to raise money for an economics prize is to consist of 8 works: 3 overtures, 4 sonatas, and a piano concerto.

(a) In how many ways can the program bearranged?

(b) In how many ways can the program be arranged if asonata must comefirst?

10. Find the number of distinguishable permutations of the letters in each word below.

(a) tilted

(b) London

(c) referred

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