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Preview File Edit View Go Tools Window Help 1esl sHomework 2.pdf (page 2 of 2) Q Search 2.pdf ways are there to form "The Whole Notes"? All 25 singers are asked to take a written music theory test. The top 6 scorers will be ranked (regardless of vocal part). f) How many possible rankings of the top 6 are there from among all the singers? Luke Skywalker is shopping for a new lightsaber because he lost his in an accident. The lightsaber store has 6 blue, 5 green, and 3 red lightsabers in stock on their shelf. The lightsabers are all identical except for color. 4. If Luke randomly picks a group of 4 lightsabers to try, what is the probability that this group has exactly 2 blue and 2 green lightsabers? If Luke randomly picks a group of 4 lightsabers to try, what is the probability that all 4 are the same color? All fourteen lightsabers are lined up randomly on a shelf at the store. What is the probability that the first and the last lightsaber are blue? How many different distinguishable ways can all fourteen lightsabers be arranged on the shelf? If all the lightsabers are lined up on the shelf, what is the probability that all the red ones are together? If all the lightsabers are lined up on the shelf, what is the probability that none of the blue ones are together? a) b) c) d) e) f) 5. wutao is working hard at his iob in the state of Washington while finishing up the writing on his PhD Items: 6696 Unread: 1616 All folders are up to date. Connected to: Purdue 1616 21

Explanation / Answer

4 ) 6 blue , 5 green 3 red

total = 6+5+3 = 14

a) 2 blue and 2 green

we have to select 2 blue from 6 blue and 2 from 5

hence

6C2 * 5C2 / 14C4

= 15 * 10 / (14*13*12*11/4!)

= 0.1498501

b)

4 are of same colour

since red colour has only 3 number < 4 , not possible

required probbaility =

(6C4 + 5C4)/14C4

= (15 +5)/14C4

= 0.01998001998

c)

first and last are blue

6 red and 8 other colour say (X)

arrangement possible =

BXXB BXBB BBXB BBBB

probability =

BXXB = 6/14 * 8/13 * 7/12 * 5/11

BXBB = 6 /14 * 8/13 * 5/12 * 4/11

BBXB = 6/14 * 5/13* 8/12*4/11

BBBB = (6*5*4*3)/(14*13*12*11)

sum = (6*8*7*5 + 2*6*8*5*4 + 6*5*4*3)/(14*13*12*11)

= 0.1648351

d)

number of ways arranged = 14!/(6!5!3!)

= 168168

Please post rest questions again

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