Question

How many 4. letter code can be
famed using the first 10 letters of
the English alphabet if no letter
can be repeated?​

Answer 1

Given that there are 10 distinct letters of the English alphabet. and we have to find how many 4 letter code can be formed using these 10 letters providing they are not repeated.

It is clear that this is a question of Permutation and we have to find the number of ways we can arrange these 10 letters.

So, We have

⇒ Distinct objects, n = 10

And, We have to form 4 letter code,

⇒ Number of letters we have to choose, r = 4

We know,

The number of objects 'r' that we can choosen out of 'n' distinct objects is given by,

⇒ ⁿPᵣ

Which is equal to,

⇒ ⁿPᵣ = n! / (n - r)!

⇒ ⁿPᵣ = 10! / (10 - 4)!

⇒ ⁿPᵣ = 10! / 6!

⇒ ⁿPᵣ = 10 × 9 × 8 × 7

⇒ ⁿPᵣ = 720 × 7

⇒ ⁿPᵣ = 5040

Hence, We can form 5040 four letter codes from 10 letters of the English alphabet without repetition.