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