Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsPermutations , combinations and binomial expansion2 Marks
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 remalning $4$ dlgits, all four can be placed in $4 P 4$ ways.
$\therefore$ Total permutations for the numbers greater than $50,000={ }^3 P_1 \times{ }^4 P_4$
$=3 \times 4!$
$=3 \times 24$
$=72$
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