how many 3 digit numbers can be formed using the digits 2,3,4. What is the probability of getting even numbers. What is the probability of getting odd numbers
Answers
Step-by-step explanation:
A three digit even number is to be formed from given 6 digits 1,2,3,4,6,7.
□□□HTO
Since, for the number is to be even , so ones place can be filled by 2,4 or 6. So, there are 3 ways to fill ones place.
Since, repetition is not allowed , so tens place can be filled by remaining 5 digits. So, tens place can be filled in 5 ways.
Similarly, hundred's place can be filled by remaining 4 digits. So, hundred's place can be filled in 4 ways.
So,required number of ways in which three digit even numbers can be formed from the given digits is 4×5×3=60
Alternative Method:
3-digit even numbers are to be formed using the given six digits, ,2,3,4,6 and 7, without repeating the digits.
Then, units digits can be filled in 3 ways by any of the digits, 2,4 or 6.
Since the digits cannot be repeated in the 3-digit numbers and units place is already occupied with a digit (which is even), the hundreds and tens place is to be filled by the remaining 5 digits.
Therefore, the number of ways in which hundreds and tens place can be filled with the remaining 5 digits Is the permutation of 5 different digits taken 2 at a time.
5P2=(5−2)!5!=3!5!
Number of ways of filling hundreds and tens place
=3!5×4×3!=20
Thus, by multiplication principle, the required number of 3-digit numbers is 3×20=60
Step-by-step explanation:
how many 3 digit numbers can be formed using the digits 2,3,4
answer: 234, 243, 324, 342, 423, 432.
What is the probability of getting even numbers.
answer: 4/6.
What is the probability of getting odd numbers
answer: 2/6