The thousands place of the 4-digit number can be filled with any digit from 1 to 9 and 0 is not included. Thus, number of ways in which thousands place is filled

is 9. Also, the hundreds, tens and units place can be filled with any digit from 0 to 9. Since, te digits cannot be repeated and thousands place is already occupied by the digit. The hundreds, tens and units place can be filled by remaining 9 digits. Thus, there are permutations of 9 different digits taken 3 at a time. Number of 3-digit numbers =

\( ^5P_4=\dfrac{5!}{(5-4)!}=\dfrac{5!}{1!}\)

= 1×2×3×4×5=120

= \( ^9P_3=\dfrac{9!}{(9-3)!}=\dfrac{9!}{6!}\)

= \(\dfrac{9\times 8\times 7\times 6!}{6!}\)

= 9×8×7=504

By, multiplication principle, number of 4-digit numbers is \( 9\times 504=4536\)

Answered by Abhisek | 1 year agoHow many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

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