Question

a password of length 4 that uses exactly 2 different digits is to be created. How many different passwords can there be?

here, 0001 is a valid password, while 3333 and 0123 are not valid passwords because they do not use exactly 2 different digits.
@cwrw238
@amistre64

Answer 1

10*10*8*8 maybe?

Answer 2

please do explain... i thought of this considering two cases , one wid 3 same and 1 same digit ,, and the other with 2 same and 2 same digits...
And the answer is to be a max of 3 digits....

Answer 3

1000 0100

1100 1010 1001
0110 0101 0011

1110 1101 1011 0111

that seems to be the set of any 2 digit combination; and to avoid using the same digit twice, there are 9 of those sets which most likely doubles the lot since the set of say 2,9 is the same as 9,2

just taking a stab at it

Answer 4

hmm, or is it 10 P 2 sets;

how many ways are there to pick 2 numbers from a set of 10 ?

Answer 5

1000 0100 0100 0001 <-- forgot to include the last 2 :)

1100 1010 1001 0110 0101 0011

1110 1101 1011 0111

Answer 6

ya there wud be 10 P 2 i.e. 10 C2 * 2! ways for picking 2 out of 10 numbers...

Answer 7

\[\left(\begin{matrix}10 \\ 2\end{matrix}\right) * (\left(\begin{matrix}4 \\ 1\end{matrix}\right) + \left(\begin{matrix}4 \\ 2\end{matrix}\right) + \left(\begin{matrix}4 \\ 3\end{matrix}\right)) = 630\]

Answer 8

i forget the setup, but spose you had 10 people, how many different groups of 2 people could you create?

Answer 9

Hey cnknd , can you explain ur method please???

Answer 10

01 02 03 04 05 06 07 08 09
12 13 14 15 16 17 18 19
23 24 25 26 27 28 29
34 35 36 37 38 39
45 46 47 48 49
56 57 58 59
67 68 69
78 79
89

45 different setups

Answer 11

ok 10 choose 2 gives u 45 combinations of 2 digits, and the other factor is what @amistre64 wrote in a previous post:
1000 0100 0100 0001
1100 1010 1001 0110 0101 0011
1110 1101 1011 0111

Answer 12

and 14 different setups for each group; 45*14 ... brute method ;)

Answer 13

O.k . thank u both, I am trying to understand the method... hoping will not face problem...

Answer 14

10 choose 2 ultimate setups

within each setup

4 choose 1 (0001 0010 0100 1000)
+
4 choose 2 (0011 0101 1001 ... )
+
4 choose 3 (1110 1101 1011 0111)

so as cnk put it

10C2 times (4C1+4C2+4C3)

Answer 15

Yes thank u so much...