Eight students compete in a tennis tournament. Each student plays each of the ot

Question

Eight students compete in a tennis tournament. Each student plays each of the other students four times. What is the total number of games played in the tournament? Robert has seven different photographs and chooses three to arrange in a display at an exhibition. How many arrangements can he make? There are six mobiles in a store. How many different arrangements of mobiles in the store are possible? What is the difference between the number of three-member committees that can be formed from a group of ten members and the total number of ways there are to arrange the members of such a committee? Scarlet is buying veggies and fruits for household purpose and must choose 4 of 6 different veggies and 2 of 3 different fruits. How many different combinations of veggies and fruits can Scarlet choose?

Explanation / Answer

1)

For 8 person, each of them plays 4*7=28 matches.
So the total number of games equals 8*28/2

= 8*14

= 112 games

" total number of games is 112 "

2)

here using permutations and combinations to answer this quations

here 3 photogrphs from 7 so we use 7c3 is the combination for arrangement

7c3= (7*6*5) / (3*2*1)

=35

3)

six mobiles in a store arrangement is 6!

6!= 6*5*4*3*2*1

= 720

4)

three members commitee from ten members is 10c3

=10*9*8/1*2*3

=120

the total commitee siting is 3!

=3*2*1

=6

the difference is 120-6

=114

5) the veggies are arranged in 6c4

= 30

the fruits are arranged in 3c2

=3

total 33 ways arranged both veggies and fruits

  

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