A locker combination system uses four digits from 0 to 9. How many different four-digit combinations are possible if the first and the last digit cannot be zero and no digit can be repeated<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n The problem asks how many different four-digit combinations can be made with the digits 0 to 9, under the condition that the first and last digits cannot be zero, and no digit can be repeated.<\/p>\n\n\n\n To solve this, let’s break it down step by step:<\/p>\n\n\n\n The first digit cannot be zero, so it can be any digit from 1 to 9. This gives us 9 possible choices for the first digit.<\/p>\n\n\n\n The second digit can be any digit from 0 to 9, except the first digit (since no digit can be repeated). Therefore, after selecting the first digit, there are 9 remaining digits to choose from.<\/p>\n\n\n\n The third digit can also be any digit from 0 to 9, except the first and second digits. This gives 8 remaining choices for the third digit.<\/p>\n\n\n\n The last digit cannot be zero, and it must also be different from the first, second, and third digits. This gives 7 remaining choices for the last digit.<\/p>\n\n\n\n To find the total number of different combinations, we multiply the number of choices for each digit: 9\u00d79\u00d78\u00d77=45369 \\times 9 \\times 8 \\times 7 = 4536<\/p>\n\n\n\n Thus, the total number of possible four-digit combinations is 4536<\/strong>.<\/p>\n\n\n\n The process of determining the number of different combinations relies on understanding the constraints of the problem:<\/p>\n\n\n\n By applying these restrictions and systematically counting the available choices for each digit position, we arrive at the final answer of 4536.<\/p>\n","protected":false},"excerpt":{"rendered":" A locker combination system uses four digits from 0 to 9. How many different four-digit combinations are possible if the first and the last digit cannot be zero and no digit can be repeated The correct answer and explanation is: The problem asks how many different four-digit combinations can be made with the digits 0 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-44271","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44271","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=44271"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44271\/revisions"}],"predecessor-version":[{"id":44273,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44271\/revisions\/44273"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=44271"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=44271"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=44271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: First digit<\/h3>\n\n\n\n
Step 2: Second digit<\/h3>\n\n\n\n
Step 3: Third digit<\/h3>\n\n\n\n
Step 4: Last digit<\/h3>\n\n\n\n
Total combinations<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
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