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permutation and combination — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSpermutation and combination1 Mark
MCQ
Five digit numbers are formed using the digits $1,2 , 3,5,7$ with repetitions and are written in descending order with serial numbers. For example, the number $77777$ has serial number $1$. Then the serial number of $35337$ is $.........$.
  • A
    $718$
  • B
    $156$
  • ✓
    $1436$
  • D
    $1472$
✓

Answer

Correct option: C.
$1436$
c
No of $5$ digit numbers starting with digit 1 $=5 \times 5 \times 5 \times 5=625$

No of $5$ digit numbers starting with digit 2 $=5 \times 5 \times 5 \times 5=625$

No of $5$ digit numbers starting with $31$ $=5 \times 5 \times 5=125$

No of $5$ digit numbers starting with $32$ $=5 \times 5 \times 5=125$

No of $5$ digit numbers starting with $33$ $=5 \times 5 \times 5=125$

No of $5$ digit numbers starting with $351$ $=5 \times 5=25$

No of $5$ digit numbers starting with $352$ $=5 \times 5=25$

No of $5$ digit numbers starting with $3531$ $=5$

No of $5$ digit numbers starting with $3532$ $=5$

Before $35337$ will be $4$ numbers,

So rank of $35337$ will be $1690$

So, in descending order serial number will be

$3125-1690+1=1436$

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