11.How many ways can two people be chosen from a group of 10 people? 12.How many

Question

11.How many ways can two people be chosen from a group of 10 people?

12.How many ways can three pizza toppings be selected from a choice of 8 pizza toppings?

13.How many ways can five eggs be selected from a basket of 12 distinct Easter eggs?

14.How many ways can a 9-person baseball' team be chosen from among a roster of 15 people?

15.How many ways can 12 books be selected from a shelf of 20 books?

16.A string of 7 characters is formed by ordering the letters ABCDEFG.

a.How many strings are possible?

b.How many strings begin and end with a vowel?

c.How many strings contain the substring ACE?

d.How many strings contain both substrings AB and FG?

17.A Halloween bag contains 10 Snickers bars, 6 Mars bars, and 5 Crunch bars.

a.How many ways can a child select three bars from the bag?

b.How many ways can a child select one of each type of bar?

c.How many ways can a child select two of each type of bar?

18.Consider an 8-bit string consisting of O's and l's.

a.How many possible strings are there?

b.How many strings contain exactly three ls?

c.How many strings begin and end with a i?

d.How many strings contain at least one 1?

Explanation / Answer

11.How many ways can two people be chosen from a group of 10 people?

this is a combination problem nCr

so 2 people can be chosen from 10 in 10C2 ways

C(n,r)=C(10,2)C(n,r)=C(10,2)

=10!(2!(102)!)=10!(2!(102)!)

= 45

12.How many ways can three pizza toppings be selected from a choice of 8 pizza toppings?

again the formula would be

8C3

C(n,r)=C(8,3)C(n,r)=C(8,3)

=8!(3!(83)!)=8!(3!(83)!)

= 56

13.How many ways can five eggs be selected from a basket of 12 distinct Easter eggs?

12C5

C(n,r)=C(12,5)C(n,r)=C(12,5)

=12!(5!(125)!)=12!(5!(125)!)

= 792

Please note that we can answer only 1 question at a time , as per the answering guidelines. I have answered 3 . Hope this helps !!

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