7E concept check
Answer the following question using the appropriate counting technique, which may be either arrangements with repetition, permutations, or combinations. Be sure to explain why this counting technique applies to the problem. How many different three-digit codes can be formed using digits 0 through 9?
Arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated.
Answer the following question using the appropriate counting technique, which may be either arrangements with repetition, permutations, or combinations. Be sure to explain why this counting technique applies to the problem. How many different three-digit codes can be formed using digits 0 through 9?
Arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated. 10^3 = 1000 possible codes
Answer the following question using the appropriate counting technique, which may be either arrangements with repetition, permutations, or combinations. Be sure to explain why this counting technique applies to the problem. How many different telephone numbers of the form aaa-bbb-cccc can be formed if the area code aaa cannot contain 7 and the prefix bbb cannot contain 1?
Arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated. There are 5,314,410,000 different telephone numbers.
Answer the following question using arrangements with repetition, permutations, or combinations. Be sure to explain why the particular counting technique applies to the problem. A dog shelter is giving away 12 different dogs, but you have room for only 55 of them. How many different dog families could you have?
Combinations should be used because no item may be selected more than once and the order does not matter. 12 C 5 = 792
Answer the following question using arrangements with repetition, permutations, or combinations. Be sure to explain why the particular counting technique applies to the problem. The President must assign ambassadors to threethree different foreign embassies. From a pool of eleveneleven candidates, how many different diplomatic teams can she form?
Permutations should be used because no item may be selected more than once and the order matters. 11 P 3 = 990
Find the probability of the given event. Choosing seven numbers that match seven randomly selected balls when the balls are numbered 1 through 37.
Therefore, the probability of choosing seven numbers that match seven randomly selected balls when the balls are numbered 1 through 37 is: 37 C 7 = 10295472 1 = -------------- 10295472
