Permutations an...

At an election, a voter may vote for any number of candidates not greater than the number to be elected. 'fhere are 10 candidates and 4 are to he elected. If a voter votes for atleast one candidate, then the number of ways in which he can vote, is

Consider the set of eight vectors

Let p be a prime number such that p ≥ 23. Let x = p! + 1. The number of primes in the list n +1, n + 2, n + 3,...., n + p – 1 is

In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amount of illumination is

The number of proper divisors of 2^p.6^q.15^r is

The number of even proper divisors of 1008 is

If one test (on screening paper basis) was conducted on Batch A, maximum number of marks is (90 × 3) = 270. 4 students get the marks lower than 80. Coaching institute decided to inform their guardians, that is why their result card were sent to their home. The number of ways, in which all the letters were put in wrong envelopes, is

The number of prime numbers among the numbers 105! + 2, 105! + 3, 105! + 4,...105! + 104 and 105! + 105 is

If eleven members of a committee sit at a round table so that the President and Secretary always sit together, then the number of arrangement is