How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

Asked by Abhisek | 1 year ago |  93

1 Answer

Solution :-

Let the five-digit number be ABCDE. Given that first 2 digits of each number is 67. Therefore, the number is 67CDE.

As the repetition is not allowed and 6 and 7 are already taken, the digits available for place C are 0,1,2,3,4,5,8,9. The number of possible digits at place C is 8. Suppose one of them is taken at C, now the digits possible at place D is 7. And similarly, at E the possible digits are 6.

The total five-digit numbers with given conditions = 8 × 7 × 6 = 336.

Answered by Pragya Singh | 1 year ago

Related Questions

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

Class 11 Maths Permutations and Combinations View Answer

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Class 11 Maths Permutations and Combinations View Answer

How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

(i) 4 letters are used at a time

(ii) all letters are used at a time

(iii) all letters are used but first letter is a vowel ?

Class 11 Maths Permutations and Combinations View Answer

There are 10 persons named P1, P2, P3 …, P10. Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.

Class 11 Maths Permutations and Combinations View Answer

How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?

Class 11 Maths Permutations and Combinations View Answer