Answer to Question #199114 in Statistics and Probability for mandona

Question #199114

A shop has 5 different printers but there is space for only 3 printers on the display shelf. How many arrangements are possible i. Suppose you have 4 different flags. How many different signals could you make using (i) 2 flags (ii) 2 or 3 flags ii. iii. How many arrangements of the letters of the word B E G I N are there if (i) 3 letters are used (ii) all of the letters are used A quiz team of four is chosen from a group of 15 students. In how many ways could the team be chosen? iv. If there are eight girls and seven boys in a class, in how many ways could a group be chosen so that there are two boys and two girls in the group? v. A school committee consists of six girls and four boys. A social sub-committee consisting of four students is to be formed. In how many ways could the group be chosen if there are to be more girls than boys in the group?


1
Expert's answer
2021-05-31T16:26:06-0400

1.

N=C533!=5!3!2!3!=60N=C^3_5\cdot3!=\frac{5!}{3!2!}\cdot3!=60


2.

i)

N=2C42=4!2!2!2=12N=2C^2_4=\frac{4!}{2!2!}\cdot2=12


ii)

N=2C42+C433!=12+4!3!3!=36N=2C^2_4+C^3_4\cdot3!=12+\frac{4!}{3!}\cdot3!=36


3.

i)

N=C533!=5!3!2!3!=60N=C^3_5\cdot3!=\frac{5!}{3!2!}\cdot3!=60


ii)

N=5!=120N=5!=120


4.

N=C154=15!11!4!=1365N=C^4_{15}=\frac{15!}{11!4!}=1365


5.

N=C72C82=7!5!2!8!6!2!=2128=588N=C^2_7\cdot C^2_8=\frac{7!}{5!2!}\cdot\frac{8!}{6!2!}=21\cdot28=588


6.

Total number of ways=number of groups with 3 girls + number of groups with 4 girls.

number of groups with 3 girls:

N1=C63C41=6!3!3!4!3!=204=80N_1=C^3_6\cdot C^1_4=\frac{6!}{3!3!}\cdot\frac{4!}{3!}=20\cdot4=80

number of groups with 4 girls:

N2=C64=6!4!2!=15N_2=C^4_6=\frac{6!}{4!2!}=15

Total number of ways:

N=N1+N2=80+15=95N=N_1+N_2=80+15=95


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