Supposed a 4-digit PIN must be formed using the digits 0 through 9. 1) How many
ID: 3422009 • Letter: S
Question
Supposed a 4-digit PIN must be formed using the digits 0 through 9.
1) How many such PINS do not repeat a digit consecutively? ie. 9129 does not repeat a digit consecutively,
even though it repeats the digit 9. However, 3341 does repeat the digit 3 consecutively.
2) How many such PINS have exactly two 2s?
3) How man such PINS have at least two 2s?
4) 5885 is a palindrome, but 1231 is not a palindrome. List every such PIN that is a palindrome. How many are there? Can you think of a more clever way to count them without list every single one?
Explanation / Answer
(1)
total number of such PINS = 10*9*9*9 = 7290
(2)
= (4c2)(9*9)
= 486
---------------
(3)
At least 2 2's = (exactly two 2's) + (excatly 3 2's) + (exactly four 2's)
= ( 486 ) + ( 4c3*9 ) + 1
= 486 + 36 + 1
= 523
-----------------------
(4)
= 10*9*1*1
= 90
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