Question

Find the number of odd integers between 30000 and 80000 in which no digit is repeated.

Answer 1

Answer:

7392

Step-by-step explanation:

odd number : ends with 1,3, 5, 7, 9

not considered : 3 * * * 3

considered : 3 * * * 1, 3 * * * 5, 3 * * * 7, 3 * * * 9 :

fill the *'s : 0 - 9 but not 1 & 3 : 8P3

hence....

all odds with 3**** : 4 × 8P3

all odds with 4**** : 5 × 8P3

all odds with 5**** : 4 × 8P3

all odds with 6**** : 5 × 8P3

all odds with 7**** : 4 × 8P3

all odds with 8***0 : 0

therefore total odds : 22 × 8P3 : 7392