Question

Find the number of n digit numbers formed using first 5 natural numbers, which contain the digits 2 and 4 essentially.​

Answer 1

Answer:

First 5 natural numbers =1,2,3,4,5

Now we have to take 2 and 4 essentially that means minimum n is 2 and maximum will be 5.

Considering digits to be non repetitive.

So, number of 2 digit numbers is 2 since only 24 and 42 are possible as it is must to take these digits

3 digit numbers:−

By permutation and combination:-

When 1 is chosen as 3rd digit:-

⇒3! numbers are possible

Similarly with 3,5

So total 3 digit numbers possible =6+6+6 =18

4 digit numbers:-

Combinations of choosing among 1,3,5= 3C2

Now, permutation possible for all combination =5!×1

Total 5 digit numbers =120

So total numbers possible =2+18+72+120=212

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Answer 2

Answer:

5^n- 4^n- 4^n+ 3^n

Step-by-step explanation:

5^n- 4^n- 4^n+ 3^n