| 31. How many two digit numbers can be generated using the digits 1,2,3,4 without repeating any digit? | |
| A. 10 | B. 12 |
| C. 4 | D. 16 |
Answer: Option B
Explanation:
We have four digits 1,2,3,4. The first digit can be any of these four digits.
Now we have already chosen the first digit. Since we cannot repeat the digits, we are left with 3 digits now. The second digit can be any of these three digits.
Since the first digit can be chosen in 4 ways and second digit can be chosen in 3 ways, both the digits can be chosen in $4×3=12$ ways. [Reference: Multiplication Theorem]
i.e., 12 two digit numbers can be formed.
sam
2015-12-20 10:41:50
but it is specified that, without repeating digits! will it not change the ans?
sam
2015-12-22 10:51:18
The digits cannot be repeated. That is why first digit has 4 options and second digit has only 3 options. Therefore 4*3=12 is the answer.
Suppose digits can be repeated. Then first digit will have 4 options. Similarly second digit also will have 4 options. In that case, answer will be 4*4=16
Simon
2015-08-21 03:58:34
This is 4p2, right?
Jay
2015-08-22 23:21:03
yes.
Add Your Comment
[use Q&A for new questions]
Name
a. repetition is allowed b. no repetition Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps[11149] You can put this solution on YOUR website! Of the 10 digits, 5 are even. So in both cases there are 5 choices for the units digit of the 2-digit number. [a] If repetition is allowed, there are 10 choices for the tens digit after the units digit is chosen. The total number of possible 2-digit numbers is 10*5 = 50. [b] If repetition is not allowed, there are only 9 choices left for the tens digit after the units digit is chosen. The total number of possible 2-digit numbers is 9*5 = 45. ------------------------------------------------- The tens digit can't be 0.... [a] If repetition is allowed, we have 5 choices for the units digit [any of the 5 even digits]; then we have 9 choices for the tens digit [any digit except 0]. That makes 5*9 = 45 2-digit numbers. [b] If repetition is not allowed, then there are two cases to consider. If the units digit is 0, then we still have 9 digits to choose from for the tens digit; that makes 9 possible 2-digit numbers with units digit 0. If the units digit is any of the other 4 even digits, then we have only 8 choices for the tens digit [it again can't be 0; and it also can't be the same as the units digit]; that makes 4*8=32 2-digit numbers with units digit 2, 4, 6, or 8. So with repetition not allowed, the total number of possible 2-digit numbers is 9+32=41. Answer by ikleyn[46139] [Show Source]: You can put this solution on YOUR
website! Of the 10 digits, 5 are even. So in both cases there are 5 choices for the units digit of the 2-digit number.
[a] If repetition is allowed, then there are 10-1 = 9 choices for the tens digit.
[9 because you can not use zero as the "tens" digit].
The total number of possible 2-digit even numbers is 9*5 = 45, if repetition is allowed.
[b] If repetition is not allowed, then there are two cases.
Case 1. The "units" digit is zero. Then you have 9 choices for the "tens" digits.
Hence, 9 [nine] 2-digit numbers are possible, ending by "0".
Case 2. The "units" digit is any of 4 even digits 2, 4, 6 or 8.
Then you have 8 choices for the "tens" digit.
[Only 8, because you can not use zero and just used "units" digit].
Hence, 8*4 = 32 2-digit numbers are possible in this case.
The total for case 1 + case 2 is 9 + 32 = 41.
So, in this problem / [sub-problem] the answer is: 41 2-digit even numbers are possible, if repetition is not allowed.
----------------- Notice that the answers to [a] and [b] are CONSISTENT: From 45 numbers of the set [a] you need exclude four numbers 22, 44, 66 and 88 to get 41 number of the set [b]. |