Question

How many four digits number can be formed if no digit can repeat?

Answer 1

Answer:

The answer is completed

Answer 2

$\huge \blue✢ \red{ \tt \underline{ Solution : - }}$

we need to find that how many 4digits number can be formed .

As we can't write 0 at thousands place beacuse of we place then it is considered as 3 digit number not 4 digit number.

So,

number of digits = 9

no of digits formed at a time = 3

$\sf \: formula = > \huge \sf \: {}^{n} P_r = \frac{n!}{(n - r)!}$

where,

• n = 9
• r = 3

$\sf \: {}^{9} P_3= \frac{9!}{(9 - 3)!} \\ \\\sf \: = \frac{9!}{6!} \\ \\ \sf \: = \frac{9 \times 8 \times 7 \times \cancel{6!}}{ \cancel{6!}} \\ \\ \sf = 9 \times 8 \times 7 \\ \\ \sf \: = 504$

Now,

When

• n = 9
• r = 1

$\sf \: {}^{9} P_1= \frac{9!}{(9 - 1)!} \\ \\\sf \: = \frac{9!}{8!} \\ \\ \sf \: = \frac{9 \times\cancel{8!}}{ \cancel{8!}} \\ \\ \sf = 9$

So,

• Number of 4digits numbers formed by digits = 504 × 9 = 4536

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