Find-the-number-of-odd-integers-between-30-000-and-80-000-in-which-no-digit-is-repeated-

Question Number 18655 by Tinkutara last updated on 26/Jul/17

Find the number of odd integers

between 30, 000 and 80, 000 in which no

digit is repeated .

Commented by mrW1 last updated on 27/Jul/17

{let}^{'} s say the number is XZZZY

X can be 3, 4, 5, 6, 7

Y can be 1, 3, 5, 7, 9

Z can be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

case 1 :

Y is one from 3 digits in {3, 5, 7}

X can be one from 4 digits : 4, 6 and 2 from {3, 5, 7}

ZZZ can be choosen from 8 digits

\Rightarrow 3 \times 4 \times 8 \times 7 \times 6

case 2 :

Y is one from 2 digits in {1, 9}

X can be one from 5 digits in [3, 7]

ZZZ can be choosen from 8 digits

\Rightarrow 2 \times 5 \times 8 \times 7 \times 6

totally

\Rightarrow 3 \times 4 \times 8 \times 7 \times 6 + 2 \times 5 \times 8 \times 7 \times 6 = 7392

Commented by mrW1 last updated on 27/Jul/17

3 \times 4 \times 8 \times 7 \times 6 + 2 \times 5 \times 8 \times 7 \times 6 = 7392

Commented by Tinkutara last updated on 27/Jul/17

Thank you very much mrW 1 Sir!