EASY
Earn 100

Six identical cards are placed on a table. Each card has the number '1'marked on one side and the number '2' marked on its other side. All the six cards are placed in such a manner that the number '1' is on the upper side. In one try, exactly four (neither more nor less) cards are turned upside down. In how many least number of tries can the cards be turned upside down such that all the sic cards show the number '2' on the upper side? 

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Important Questions on Permutation and Combination

MEDIUM
The number of distinct primes dividing 12!+13!+14! Is
MEDIUM
How many natural numbers n are there such that n!+10 is a perfect square ?
EASY
If Pr+656:Pr+3=30800:154 , then r is equal to
MEDIUM
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:
EASY
The number of ways in which 5 girls and 3 boys can be seated in a row so that no two boys are together is
MEDIUM
The largest non-negative integer k such that 24k divides 13! is
MEDIUM
The number of all 3-digits numbers abc (in base 10) for which 10 is
HARD
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4  taken all at a time. The number of such numbers in which the odd digits occupy even places is
EASY
The number of ways in which 3 prizes can be distributed to 4 children, so that no child gets all the three prizes, are
EASY
Ten different letters of an alphabet are given, words with five letters are formed from these given letters. Then, the number of words which have at least one letter repeated is
EASY
The sum of the digits in the unit's place of all the 4 - digit numbers formed by using the numbers 3, 4, 5 and 6, without repetition is :
EASY

In how many ways the letters of word 'MACHINE' can be arranged so that vowels will always be together?

MEDIUM
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:
MEDIUM
How many ways are there to arrange the letters of the word EDUCATION so that all the following three conditions hold?
- the vowels occur in the same order EUAIO,
- the consonants occur in the same order DCTN,
- no two consonants are next to each other.
HARD
If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is 
MEDIUM
The number of four-digit numbers strictly greater than 4321 that can be formed using the digit 0,1,2,3,4,5 (repetition of digits is allowed) is:
MEDIUM
The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is
MEDIUM
Two girls and four boys are to be seated in a row in such a way that the girls do not sit together. In how many different ways can it be done?
EASY
Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is
EASY

How many numbers of four digits can be made by using the digits 3, 5, 6, 7, and 9?  (Repetition of digits is not allowed)