1. For a group photograph, 3 boys and 4 girls stand in a line in all possible ways. How many photos could be taken if each photo corresponds to each such arrangement?
(a) 2656
(b) 6600
(c) 3540
(d) 5040
(e) 5130
2. A team of 16 cricketers is selected for the ODI series. It consists of 10 old players and 6 new players. As a principle, it was decided that the team playing any of the matches must contain 8 old players and 3 new players. The number of ways the team can be selected, is
(a) 1250
(b) 900
(c) 850
(d) 450
(e) None of these
3. The number of 3-digit numbers which can be formed from the digit 1, 2, 3, 4 and 5 if repetition of digits is allowed, is
(a) 15
(b) 125
(c) 5!
(d) 3!
(e) None of these
4. Find the number of ways of arranging 6 boys and 4 girls in a row so that all the girls sit together.
(a) 7! × 4!
(b) 7 × 4!
(c) 7! × 4
(d) 7! × 4! × 2!
(e) None of these
5. Out of 8 men and 5 women, a committee of 5 is to be formed. Find the number of ways in which this can be done so as to include at least 3 women.
(a) 328
(b) 326
(c) 324
(d) 322
(e) None of these
6. Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman, is
(a) 25/39
(b) 14/35
(c) 5/13
(d) 10/13
(e) 1/2
7. The probability that a man can hit a target is ¾. He tries 5 times. The probability that he will hit the target at least three times, is
(a) 291/364
(b) 371/464
(c) 471/502
(d) 459/512
(e) None of these
8. A bag contains 12 white and 18 black balls. Two balls are drawn in succession without replacement. What is the probability that first is white and second is black?
A) 36/135
B) 36/145
C) 18/ 91
D) 30/91
E) None of these
9. An elevator starts with 5 passengers and stops at 8 different floors of the house. Find out the probability of all the 5 passengers alighting at different floors.
(a) 101/512
(b) 105/512
(c) 107/512
(d) 109/512
(e) None of these
10. If a 4-digit number is formed at random using the digits 1, 3, 5, 7 and 9 without repetition, then the probability that it is divisible by 5, is
(a) 4/5
(b) 3/5
(c) 1/6
(d) 2/3
(e) 1/5
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