How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
The given digits are 1, 2, 3, 4, 5 and 6.
There are many ways to form 3-digit even numbers from the digits 1, 2, 3, 4, 5 and 6. Since even numbers contain even digits in it unit’s place and there are three even digits in the given digits that are 2, 4 and 6.So, unit’s place can be filled by any one of these 3 digits. The number of ways to fill the units place is 3.
Since, there are no restrictions for the rest two places and the repetition of digits are also allowed, then the ten’s place can be filled by any of the 6 digits. Thus the possible ways to fill the ten’s place is 6. In the same way, hundred’s place can also be filled by any of the given 6 digits.
The total number of ways of forming 3-digit numbers from the given digits can be given by multiplication principle which states that if an event can occur in m different ways and follows another event that can occur in n different ways, then the total number of occurrence of the events in the given order is m × n .
The total number of ways to form a 3-digit even number is,
3 × 6 × 6 = 108
Thus, 3-digit even number can be formed in 108 ways.
The given digits are 1, 2, 3, 4, 5 and 6.
There are many ways to form 3-digit even numbers from the digits 1, 2, 3, 4, 5 and 6. Since even numbers contain even digits in it unit’s place and there are three even digits in the given digits that are 2, 4 and 6.So, unit’s place can be filled by any one of these 3 digits. The number of ways to fill the units place is 3.
Since, there are no restrictions for the rest two places and the repetition of digits are also allowed, then the ten’s place can be filled by any of the 6 digits. Thus the possible ways to fill the ten’s place is 6. In the same way, hundred’s place can also be filled by any of the given 6 digits.
The total number of ways of forming 3-digit numbers from the given digits can be given by multiplication principle which states that if an event can occur in m different ways and follows another event that can occur in n different ways, then the total number of occurrence of the events in the given order is
The total number of ways to form a 3-digit even number is,
Thus, 3-digit even number can be formed in 108 ways.
