Question

# Six-digit odd numbers, greater than 6,00,000 that can be formed using the digits 5,6,7,8,9 and 0 if repetition of digits is not allowed is :

A
60
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B
240
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C
560
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D
4×65
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Solution

## The correct option is B 240We have 6 digits, 5,6,7,8,9 and 0 and we have to form odd numbers greater than 6,00,000 The unit's place can only be filled by 5,7 or 9 since we have to form odd numbers. The first place (lakh's position) can be occupied by the digits greater than or equal to 6. Since, repetition is not allowed, therefore - Digits in lakh's placeDigits in the unit's place(I)65,7,9(II)75,9(III)85,7,9(IV) 95,7 Thus the required six digit numbers possible are (I) 4!+4!+4! (II) 4!+4! (III) 4!+4!+4! (IV) 4!+4! =10×4!=240

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2