How many 7-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 1234321. Answers.
A) 100  B) 610  C) 729  D) 9000  E) 1000
Take the task of building palindromes and break it intostages.   Stage 1: Select the 7th digit   We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 1 in 9ways   Stage 2: Select the 6th digit   We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 2 in10ways   Stage 3: Select the 5th digit   We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 3 in10ways   Stage 4: Select the 5th digit   We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9   So, we can complete stage 4 in10ways   IMPORTANT: At this point, the remaining digits are alreadylocked in.   Stage 5: Select the hundreds digit   This digit must be the SAME as the thousands digit (which we already chose in stage 2)   So, we can complete this stage in1way.   Stage 6: Select the tens digit   This digit must be the SAME as the thousands digit (which we already chose in stage 2)   So, we can complete this stage in1way.   Stage 7: Select the units digit   This digit must be the SAME as the ten-thousands digit (which we already chose in stage 1)   So, we can complete this stage in1way.   By theFundamental Counting Principle(FCP), we can complete all 5 stages (and thus build a 7-digit palindrome) in(9)(10)(10)(10)(1)(1)(1)ways (= 9000 ways)   Answer: 9000
<result>D</result>
How many 7-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 1234321.