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STD 11 - 6. permutation and combination — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 6. permutation and combination4 Marks
MCQ
How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ each digit appearing not more than once in each number
  • ✓
    $5{ \times ^8}{P_3}$
  • B
    $5{ \times ^8}{C_3}$
  • C
    $5\;!\;{ \times ^8}{P_3}$
  • D
    $5\;!\;{ \times ^8}{C_3}$
✓

Answer

Correct option: A.
$5{ \times ^8}{P_3}$
a
(a) A number between $5000$ and $10,000$ can have any of the digits $5, 6, 7, 8, 9$ at thousand's place.

So thousand's place can be filled in $5$ ways.

Remaining $3$ places can be filled by the remaining $8$ digits in $^8{P_3}$ ways

. Hence required number = $5{ \times ^8}{P_3}$.

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