Solve ques 3 Q 3 n-digit numbers are formed using only three digits 2, 5 and 7 The - Maths - Permutations and Combinations

Question

Solve ques 3
Q 3 n-digit numbers are formed using only three digits 2, 5 and 7
The smallest value of n for which 900 such distinct numbers can be
formed, is
(A) 6
(B) 7
(C) 8
(D) 9

Sandeep Saurav · Accepted Answer

Dear Student,

If It is one digit number there will be 31 such numbers (as in that one digit there can either be 2, 5 or 7)If It is two digit number there will be 32 such numbers (as in that ones place there can either be 2, 5 or 7 and in tens place there can either be 2, 5 or 7 too so, 3×3=32 such numbers)
If It is n digit number there will be 3n such numbersNow,According to question,3n>900⇒log33n>log3900⇒n log33>6
1918⇒n>6
1918and n is an integerso, smallest value of n will ne integer just after 6
1918, i e  7
Regards

Solve ques 3 Q.3. n-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is (A) 6 (B) 7 (C) 8 (D) 9

Solve ques 3
Q.3. n-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is
(A) 6
(B) 7
(C) 8
(D) 9