How many three digit even number are possible when:- (i)Repeatation not allowed (ii) Repeatation allowed?

Question

Answer

When repeatition is allowed then no. of digits formed= 9*10*10= 900...When repeatition not is allowed then no. of digits formed=9*9*8=648.

Answer

(I)8x8x4+9x8x1=328(ii)total 3 digit number of ways when R.A.=900So,total even no. Of 3 digit=900/2=450

Answer

When Repeatation not allowed:

• To form a three-digit even number when repetition is not allowed, we first need to consider the possible choices for each digit.
• For the hundreds place, we have 4 choices (2, 4, 6, 8) since the number has to be even.
• For the tens place, we have 9 choices (0-9 excluding the digit already used in the hundreds place) as zero cannot be the leading digit.
• For the units place, we have 8 choices (0-9 excluding the two digits already used).
• Therefore, the total number of three-digit even numbers without repetition is 4 x 9 x 8 = 288.

When Repeatation allowed:

• To form a three-digit even number when repetition is allowed, we can have zero in any place as the leading digit.
• For the hundreds place, we have 4 choices (0, 2, 4, 6, 8).
• For the tens and units place, we have 10 choices each (0-9).
• Therefore, the total number of three-digit even numbers with repetition allowed is 4 x 10 x 10 = 400.

In summary, when repetition is not allowed, there are 288 three-digit even numbers possible, and when repetition is allowed, there are 400 three-digit even numbers possible.

Top Courses for Class 11View all

Chemistry Class 11

CUET Mock Test Series

English Class 11

Chemistry Practice Tests: CUET Preparation

CUET Mock Test: Humanities Subjects 2025

Top Courses for Class 11

Top Courses for Class 11

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams