In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be allotted to six persons, one person occupying one room only, the number of ways in which this can be done so that no floor remains empty is a. `"^8P_6-2(6!)` b. `"^8P_6` c. `"^8P_5(6!)` d. none of these

Among 10 persons, A, B, C are to speak at a function. The number of ways in which it can be done if A wants to speak before B and B wants to speak before C is a. 10 !//24 b. 9!//6 c. 10 !//6 d. none of these

Total number of six-digit number in which all and only odd digits appear is a. 5/2(6!) b. 6! c. 1/2(6!) d. none of these

In an election, the number of candidates is one greater than the persons to be elected. If a voter can vote in 254 ways, the number of candidates is a. 7 b. 10 c. 8 d. 6

A seven-digit number without repetition and divisible by 9 is to be formed by using seven digits out of 1, 2, 3, 4 5, 6, 7, 8, 9. The number of ways in which this can be done is (a) 9! (b) 2(7!) (c) 4(7!) (d) non of these

In how many ways can a party of 6 men be selected out of 10 Hindus, 8 Muslims, and 6 Christians? If the party consists of at least one person of each religion, find the number of ways of selection. (Consider only the religion of the person).

The number of terms of an A.P. is even; the sum of the odd terms is 24, and of the even terms is 30, and the last term exceeds the first by 21/2 then the number of terms in the series is 8 b. 4 c. 6 d. 10

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4, and then the men select th chairs from amongst the remaining. The number of possible arrangements is a. ^6C_3xx^4C_2 b. ^4P_2xx^4P_3 c. ^4C_2xx^4P_3 d. none of these

A bag contains an assortment of blue and red balls. If two balls are drawn at random, the probability of drawing two red balls is five times the probability of drawing two blue balls. Furthermore, the probability of drawing one ball of each color is six time the probability of drawing two balls. The number of red and blue balls in the bag is a. 6,3 b. 3,6 c. 2,7 d. none of these

The sum of all four-digit numbers that can be formed by using the digits 2, 4, 6, 8 (when repetition of digits is not allowed) is a. 133320 b. 5333280 c. 53328 d. none of these