chawlavinu wrote:
x2suresh wrote:
dancinggeometry wrote:
What is the greatest number of four-digit integers whose unit’s digit must be 1, hundred’s digit must be even, if no repetition of digits is allowed?
360
256
252
250
212
XEX1
= No.of ways if thousands digit is odd + No. Of ways if thousands digit is even
= 4*5*7*1+ 4*4*7*1
= 36*7
=252
x2Suresh,
Can you please elobarate your explanation? I did not understand even a bit of it.
Let me explain,
we are encountering with 2 situations:
1- No. of ways if
thousands digit is odd:
---- For thousands digit: 5 potential digits can stand in it: 1 - 3 - 5 - 7 - 9 , but according to the question digit 1 is placed in the "Unit digit". So we have just
4 different alternatives for thousands digit.
---- For hundreds digit: this digit should be even. so we have
5 alternatives: 0 - 2- 4- 6- 8
---- For unit digit: we should put just "1" in this place and nothing else. so we have just
1 option.
---- For tens digit: we can put every digit (but not "1") in this place. but we know that no repetition of digits is allowed. we potentially have 0, 1, ..., 9 options. but "1" is allocated to units digit, and 2 other digits are allocated to hundreds and thousands digits. So we have
7 (10-3=7) options to place in tens digits.
the total possibilities is made by multiplying these alternatives: 4 * 5 * 7 * 1
2- No. of ways if thousands digit is even:
---- For thousands digit: 4 Alternative (we can not use "0" for this place)
---- For hundreds digit: 4 alternatives (basically we have 5 options, but we use one of them in the thousands digit, so we have 4 other options)
---- For unit digit: we have just one option (1)
---- For tens digit: we have 10-3=7 alternatives
the total possibilities: 4 * 4 * 7 * 1
Totally, we should add: 4*5*7*1+4*4*7*1=252
Hope it would help you