How many possible 3 digit password can be formed from numbers 0 to 3 without repetition
So basically, I attempted this question as- There are 4 numbers and 3 places to put in the numbers: In the ones place, any 4 numbers can be put, so there are 4 choices in the ones place. Similarly for the tens and the hundreds place. So, the total choices are, by multiplication principle- $$4*4*4=64$$ And well and good, this was the answer. But what if I reversed the method? So I take some particular numbers, like $1,2,3$ and say that, well, $1$ can go in $3$ places, $2$ in $2$ places and $3$ in $1$ place, so by multiplication principle, there are $6$ ways of forming a $3$-digit number with $1,2,3$. But there are $4$ different numbers. So the number of $3$-number combinations are- $(1,2,3)$,$(1,2,4)$,$(1,3,4)$,$(2,3,4)$. Each can be arranged in $6$ ways, so we get $24$ ways totally. So why is my answer different here? Problem 1: How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that –(i) repetition of the digits is allowed?Solution:
(ii) repetition of the digits is not allowed?Solution:
Problem 2: How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?Solution:
Problem 3: How many 4-letter code can be formed using the first 10 letters of the English alphabet if no letter can be repeated?Solution:
Problem 4: How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?Solution:
Problem 5: A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?Solution:
Problem 6: Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?Solution:
How many 3 digit numbers can be formed if repetition is not allowed?There are 504 different 3-digit numbers which can be formed from numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 if no repetition is allowed. Note: We can also use the multiplication principle to answer this question.
How many 3 digit numbers can be formed using 0 9 if repetition is allowed?We have to find the number of arrangements of 3 digits which can be formed from digits 0 to 9. Therefore, in 1000 arrangements 3 digits can be formed from the digits 0 through 9.
How many passwords can you make with 3 numbers?Therefore in that set of 720 possibilities, each unique combination of three digits is represented 6 times. So we just divide by 6. 720 / 6 = 120. That's your answer.
How many 3 digit numbers can be formed from the digits 12345 without repetition?Thus, The total number of 3-digit numbers that can be formed = 5×5×5 = 125.
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