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How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
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Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
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Find the number of ways in which one can post 5 letters in 7 letter boxes ?
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Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
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Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
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In how many ways can 5 different balls be distributed among three boxes?
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In how many ways can 7 letters be posted in 4 letter boxes?
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In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
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There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
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Let P(n) be the statement : 2n ≥ 3n. If P(r) is true, show that P(r + 1) is true. Do you conclude that P(n) is true for all n ∈ N?
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\[\frac{(2n)!}{2^{2n} (n! )^2} \leq \frac{1}{\sqrt{3n + 1}}\] for all n ∈ N .
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Evaluate each of the following:
8P3
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Evaluate each of the following:
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x2n−1 + y2n−1 is divisible by x + y for all n ∈ N.
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Evaluate each of the following:
6P6
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Evaluate each of the following:
P(6, 4)
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