close
標題:
probability question2
發問:
Problem 2: A base ten number is a string of five digits, where the digits are from theset {1.... 9} but the rst digit cannot be 0 (so 52375 is a valid numberbut 02323 and 2323 are not).(a) How many five-digit base ten numbers are there?(b) How many five-digit numbers have no two consecutive digits equal?(c)... 顯示更多 Problem 2: A base ten number is a string of five digits, where the digits are from the set {1.... 9} but the rst digit cannot be 0 (so 52375 is a valid number but 02323 and 2323 are not). (a) How many five-digit base ten numbers are there? (b) How many five-digit numbers have no two consecutive digits equal? (c) How many have at least one pair of consecutive digits equal?
最佳解答:
a) 9 possible numbers for each digits :9 * 9 * 9 * 9 * 9 = 9? = 59049 numbers. b)Case 1 : For no repeat digits , 9P5 = 15120 numbers. Case 2 : 1 pair repeat digits (AA) (9 ways) and have no two consecutive digits equal : ( ) B ( ) C ( ) D ( ) , choosing 2 ( ) fill A in them : 4C2 ways , B,C,D : 8P3 ways ,9 * 4C2 * 8P3 = 9 * 6 * 336 = 18144 numbers in this case. Case 3 : 3 repeat digits(AAA) (9 ways) or 3 repeat digits plus a pair repeat digits , and have no two consecutive digits are equal : A ( ) A ( ) A 8 possible numbers for each ( ) .9 * 8 * 8 = 576 numbers in this case. Total : 15120 + 18144 + 576 = 33840 numbers. c)59049 - 33840 = 25209 numbers.
其他解答:
probability question2
發問:
Problem 2: A base ten number is a string of five digits, where the digits are from theset {1.... 9} but the rst digit cannot be 0 (so 52375 is a valid numberbut 02323 and 2323 are not).(a) How many five-digit base ten numbers are there?(b) How many five-digit numbers have no two consecutive digits equal?(c)... 顯示更多 Problem 2: A base ten number is a string of five digits, where the digits are from the set {1.... 9} but the rst digit cannot be 0 (so 52375 is a valid number but 02323 and 2323 are not). (a) How many five-digit base ten numbers are there? (b) How many five-digit numbers have no two consecutive digits equal? (c) How many have at least one pair of consecutive digits equal?
最佳解答:
a) 9 possible numbers for each digits :9 * 9 * 9 * 9 * 9 = 9? = 59049 numbers. b)Case 1 : For no repeat digits , 9P5 = 15120 numbers. Case 2 : 1 pair repeat digits (AA) (9 ways) and have no two consecutive digits equal : ( ) B ( ) C ( ) D ( ) , choosing 2 ( ) fill A in them : 4C2 ways , B,C,D : 8P3 ways ,9 * 4C2 * 8P3 = 9 * 6 * 336 = 18144 numbers in this case. Case 3 : 3 repeat digits(AAA) (9 ways) or 3 repeat digits plus a pair repeat digits , and have no two consecutive digits are equal : A ( ) A ( ) A 8 possible numbers for each ( ) .9 * 8 * 8 = 576 numbers in this case. Total : 15120 + 18144 + 576 = 33840 numbers. c)59049 - 33840 = 25209 numbers.
其他解答:
此文章來自奇摩知識+如有不便請留言告知
文章標籤
全站熱搜
留言列表
