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How many four-digit numbers Will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition? - Mathematics and Statistics

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Sum

How many four-digit numbers Will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?

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Solution

Among many sets of digits, the greatest number is possible when digits are arranged in descending order.
∴ 7432 is the greatest number, formed from the digits 2, 3, 4, 7.
∴ Since a 4-digit number is to be formed from the digits 2, 3, 4, 7, where repetition of digit is not allowed.
∴ 1000’s place digit can be selected in 4 ways.
100’s place digit can be selected in 3 ways.
10’s place digit can be selected in 2 ways.
Unit’s place digit can be selected in 1 way.
∴ Total number of numbers not exceeding 7432 that can be formed from the digits 2, 3, 4, 7
= Total number of four-digit numbers formed from the digits 2, 3, 4, 7
= 4 × 3 × 2 × 1 = 24

Concept: Concept of Multiplication Principle
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.1 | Q 11 | Page 73
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