Required probability = 1- probability that all the boys sit together
= 1- 1/42 = 41/42
Required probability = 1- probability that all the girls sit together
= 1 - 1/42 = 41/42
Total number of ways of selection of 3 marbles out of 12
= n(S) = 12C3 = 220
Total number of favorable events = n(E)
= 3C3 + 4C3 = 1 + 4 = 5
? Required probability
= 5/220 = 1/44
Total number of caps = 12
n(s) = 12c1 = 12
Out of ( 2 blue + 1 yellow) caps, number of ways to pick one cap n(E) = 3c1 = 3
? Required probability = p(E) = n (E) / n(s) = 3/12 = 1/4
Required probability = favorable number of cases/ total number of
=8P5 / 8 5 = 105/512
Total number of possible arrangement for 4 boy and 3 girls in a queue = 7!
when they occupy alternate position then the arrangement would be like
BGBGBGB. Thus the total number of possible arrangement = 4! x 3!
? Required probability = 4! x 3! / 7!
= (4 x 3 x 2 x 3 x 2) / (7 x 6 x 5 x 4 x 3 x 2) = 1/35
We have, 5 boys and 5 girls.
Since, all the girls are sitting together, we consider them as one. Now, we can arrange 5 boys and 1 girl in 6! ways and these 5 girls (whom we considered as one) can also be arranged in 5! ways.
? Favorable number of ways = 6!5!
and total number of ways to arrange 5 boys and 5 girls = 10!
? Required probability 6!5!/10! = 1/42
Required probability = 6!5!/10! = 1/42
n(S) = 2100
n(E) = No. of favourable ways = 100C1 + 100C3 + ... 100 C99 = 2100-1 = 299
[? nC1 + nC3 + nC5 + ........................... = 2n-1 ]
? P(E)= n(E)/n(S) = 299/2100 = 1/2
Note : The given case can be generalised as "If a unbiased coin is tossed 'n' times, then the chance that the head will present itself an odd number of times is 1/2. "
Total possible ways of selecting 4 students out of 15 students = 15C4
= (15 x 14 x 13 x 12) / (1 x 2 x 3 x 4) = 1365
The no. of ways of selecting 4 students in which no students belongs to karnataka = 10C4
? Number of ways of selecting atleast one student from karnataka = 15C4 - 10C4 = 1155.
? Required probability
= 1155 / 1365 = 77 / 91 = 11 / 13
n(S) = 12C3 = (12 x 11 x 10) / (3 x 2) = 2 x 11 x 10 = 220
No. of selecting of 3 oranges out of the total 12 orange = 4C3 = 4
? n(E) = No. of desired selection of oranges = 220 - 4 = 216
? P(E) = n(E) / n(S) = 216 / 220 = 54/55
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