how many 4 digit numbers can you form with (1,2,3,4,5,6,7) ? (No repeated numbers)
The answer is 840 (7P4)
BUT
How many of these are odd numbers?
I know that there are 4 odd numbers...
Hello, Faisal2007!
How many 4-digit numbers can you form with (1,2,3,4,5,6,7) ?
(No repeated numbers)
The answer is: .$\displaystyle _7P_4 = 840$
But how many of these are odd numbers?
The last (rightmost) digit must be odd; there are $\displaystyle {\color{blue}4}$ choices: 1, 3, 5, or 7.
The other three digits are chosen from the remaining six digits: .$\displaystyle _6P_3 = {\color{blue}120}$ ways.
Therefore, there are: .$\displaystyle 4\cdot120 \:=\:480$ odd numbers.