(6) Let\'s count! (You DO NOT need to simplify your answers) (a) How many differ
ID: 2932664 • Letter: #
Question
(6) Let's count! (You DO NOT need to simplify your answers) (a) How many different cannot be 0 or 1? t seven-digit telephone numbers are possible if the first digit n (b) A multiple-choice test consists of ten questions with choices a, b, c, d, and e. How many diferent answer keys are possible? (c) How many words can be found be arranging the letters in CINCINNATI? (d) How many ways can 6 people stand in line at the grocery store if Elizabeth and her son, Samuel are together in the front of the line? (e) How many ways can 6 people stand in line at the grocery store if Elizabeth and her son, Samuel must stand together?Explanation / Answer
Solution :
( a )
the number of different seven digit numbers possible and the first digit should not be 1 or 0
= 8 * 106
( b )
the number of different answer keys for ten question which have five options = 510 = 9765625
( c )
the number of different word obtained arranging CINCINNATI = 10! / ( ( 2! ) ( 3! ) ( 3! )
= 50400
( d )
the number of ways of six people standing in a line where elizabeth and samule stand together in the front
= 2 * 4!
= 48
( e )
the number of ways of six people standing in a line where elizabeth and samule stand together =2 * 5!
= 240
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