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How many motor vehicle registration number plates can be formed with the digits (1, 2, 3, 4, 5) if the registration number can have 1 to 5 digits? (No repeated digits allowed)

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Important Questions on Permutations and Combinations

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There are 25 points on a plane of which 7 are collinear. Find how many quadrilaterals can be formed from these points?
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There are ten subjects in the school day at St. Vincent's High School, but the sixth standard students have only 5 periods in a day. In how many ways can we form a timetable for the day for the sixth standard students if no subject is repeated?
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There are 8 Consonants and 5 Vowels in a word jumble. In how many ways can we form 5-letter words having 3 Consonants and 2 Vowels?
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How many batting orders are possible for the Indian cricket team if there is a squad of 15 to choose from such that Sachin Tendulkar is always chosen?
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There are 5 blue socks, ⁣4 red socks and 3 green socks, all different in Debu's wardrobe. He has to select 4 socks from this set. In how many ways can he do so?
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A class prefect goes to meet the principal every week. His class has 30 people apart from him. If he has to take groups of three every time he goes to the principal, in how many weeks will he be able to go to the principal without repeating the group of same three which accompanies him?
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A class prefect goes to meet the principal every week. His class has 30 people apart from him. If he has to take groups Of three every time he goes to the principal,
If on the very first visit the principal appoints one of the boys accompanying him as the head boy of the school and lays down the condition that the class prefect has to be accompanied by the head boy every time he comes then for a maximum of how many weeks (including the first week) can the class prefect ensure that the principal sees a fresh group of three accompanying him?
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How many distinct words can be formed out of the word PROWLING which start with R & end with W?