Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsPermutations , combinations and binomial expansion1 Mark
Question
Using all the digits $2, 3, 5, 8, 9,$ how many numbers greater than $50,000$ can be formed ?
✓
Answer
Given digits are $2, 3, 5, 8, 9.$
For the numbers greater than $50,000$ the digit at the first place may be $5$ or greater than it.
$\therefore$ Out of the digit $5,8,9$, the first digit can be placed in ${ }^3 P_1$ ways.
Now, from the remaining $4$ digits, all four can be placed in ${ }^4 P_4$ ways.
$\therefore$ Total permutations for the numbers greater $50,000={ }^3 P_1 \times{ }^4 P_4=3 \times 4!=3 \times 24=72$
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