How many distinct odd-digit numbers can be written with the digits 1,2,3, 4 and 5 if no digit may be used more than once?
+526 Digits are 1, 2, 3, 4 and 5.
⇒no. of 1-digit odd no.'s = 3
[Repetition of digits not allowed]
No. of 2-digit odd numbers
one's place has = 3 possibilities
Then, 10's place has = 4 possibilities
⇒ no. of 2-digit odd numbers = 4 × 3 = 12
No. of 3-digit odd numbers
one's place has = 3 possibilities
10's place has = 4 possibilities
then, 100's place has = 5 - 2 = 3 possibilities
⇒ no. of 3-digit odd numbers = 3 × 4 × 3 = 36
No. of 4-digit odd numbers
one's place has = 3 possibilities
10's place has = 4 possibilities
100's place has = 3 possibilities
then, 1000's place has = 2 possibilities
⇒ no. of 4-digit odd numbers = 3 × 4 × 3 × 2 = 72
No. of 5-digit odd numbers
one's place has = 3 possibilities
10's place has = 4 possibilities
100's place has = 3 possibilities
1000's place has = 2 possibilities
then, 10000's place has = 1 possibility
⇒ no. of 5-digit odd numbers = 3 × 4 × 3 × 2 × 1 = 72
∴ No. of odd numbers = 72 + 72 + 36 + 12 + 3 = 195
