Fiona writes a list containing all the four-digit numbers that can be written using only the digits 1, 2, and 3. What is the probability that a randomlychosen number in Fiona's list has a digit-sum that is at least 6?
For example, 1,322 is such a number scine 1+3+2+2=8 is at least 6.
+9674 It is quite complicated to consider those numbers which have a digit sum that is at least 6.
We can consider those numbers which have a digit sum less than 6 instead.
Numbers with digit sum 4: 1111
Numbers with digit sum 5: 2111, 1211, 1121, 1112
Therefore, there are only 5 numbers with a digit sum less than 6. All other numbers have a digit sum of at least 6.
Note that there are 3^4 = 81 numbers which can be written with only 1, 2, 3.
\(\text{Required number} = 3^4 - 5 = 76\).
+9674 It is quite complicated to consider those numbers which have a digit sum that is at least 6.
We can consider those numbers which have a digit sum less than 6 instead.
Numbers with digit sum 4: 1111
Numbers with digit sum 5: 2111, 1211, 1121, 1112
Therefore, there are only 5 numbers with a digit sum less than 6. All other numbers have a digit sum of at least 6.
Note that there are 3^4 = 81 numbers which can be written with only 1, 2, 3.
\(\text{Required number} = 3^4 - 5 = 76\).
