From the given digit 1 2 3 4 5 6 how many three digit number could be made such that

The above digits are arranged in 123,135,234,246,345,456,654,543,642,432,531,321
so there 12 numbers
11 years agoHelpfull: Yes(33) No(4)

A total of 12 digit is formed which will be in AP.
123,321, 135,531, 234,432, 345,543, 456,654
11 years agoHelpfull: Yes(5) No(0)
12 numbers
11 years agoHelpfull: Yes(3) No(0)
1 2 3 .....3! ways to arrange
2 3 4.....3!
3 4 5 .....3!
4 5 6....3!
1 3 5....3!
2 4 6....3!

so 6 x 3! = 36
11 years agoHelpfull: Yes(3) No(15)
arshal jain if 123 is arranged then 213 is not in AP.so it should not be counted
11 years agoHelpfull: Yes(3) No(0)
AP can be formed in 18 ways
Case 1:(6)
diff=0
111,222,333,444,555,666
Case 2:(4)
diff = 1
123,234,345,456
Case 3:(2)
diff = 2
135,246
Case 4 (4)
diff= -1
654,543,432,321

case 5 (2)
diff=-2
642,531

So total :
6+4+2+4+2=18
11 years agoHelpfull: Yes(2) No(1)
@ jigneshkoradiya 145,156,....etc etc doesn't come under AP(ARITHEMATIC PROGRESSION)
11 years agoHelpfull: Yes(1) No(0)
total cases:
111,123,135
210,222,234,246
321,333,345
420,432,444,456
531,543,555
630,642,654,666
total cases=21
11 years agoHelpfull: Yes(1) No(6)
@RAJKUMAR why you do not count the 145,156,....etc etc???
11 years agoHelpfull: Yes(0) No(1)
121,122,123,124,125,126
121,123,125
121,124
11 years agoHelpfull: Yes(0) No(3)
@JIGNESHKORADIYA the numbers 145,156 are not in AP...The numbers you mentioned below are not in AP and there common difference is not same
11 years agoHelpfull: Yes(0) No(0)
@rajkumar thanks for this explaination.......!!!!
11 years agoHelpfull: Yes(0) No(0)
12 cases are possible
11 years agoHelpfull: Yes(0) No(0)
Total of 12 numbers can be made !!!
11 years agoHelpfull: Yes(0) No(0)

From the given digit 1,2,3,4,5,6 how many three digit number could be made such that the three digit used must be in AP.