Permutations And Combinations

Question
CBSEENMA11014116

How many different numbers of 5-digit can be formed by using the digits 2,3, 4, 5 and 7, without repetition, so that the number is not divisible by 5?

Solution

Number of digit available = 5 (all distinct)
Number of digits to be used = 5
                   
Since the number is not divisible by 5.
rightwards double arrow   5 cannot occupy box 5.
       Number of permutations for box 5 equals straight P presuperscript 4 subscript 1 space equals space fraction numerator 4 factorial over denominator 3 factorial end fraction equals 4                      ...(i)
       Now, we have 4-digits and 4 boxes.
        Number of permutations = straight P presuperscript 4 subscript 4 space equals space 4 factorial space equals space 24                                ... (ii)
        From (i) and (ii), the total number of permutations = 4 x 24 = 96
        Hence, the number of numbers formed, that are not divisible by 5 = 96.
        

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