What is the probability that the arrangement has both consecutive W's and consecutive Y's in WYSIWYG?

**Ans. 0.0952**This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

What is the probability that the arrangement has both consecutive W's and consecutive Y's in WYSIWYG?

**Ans. 0.0952**

In how many ways may fifty-two cards be divided amongst tour players, so that each may have thirteen ?

**Ans. $\frac{52!}{(13!)^4}$**

In how many ways can three boys divide twelve oranges, each taking four, the oranges being all of different sizes ?

**Ans. 34650**

Four flags are to be hoisted on one mast, and there are twenty different flags to choose from : what choice have we ?

**Ans. 116280**

Probability of n Heads in 2n Tosses of a Coin?

Ans. $\frac{(2n)!}{{(n!)^2}{2^{(2n)}}}$

Ans. $\frac{(2n)!}{{(n!)^2}{2^{(2n)}}}$

In how many ways can the following letters be divided between two persons :

a, a, a, a, b, b, b, c, c, d?

**Ans. 118**

a, a, a, a, b, b, b, c, c, d?

In how many ways can six different things be divided into two parcels ?

**Ans. 31**

There are twenty candidates for an office, and seven electors. In how many ways can the votes be given ?

In how many ways can you arrange on a shelf 6 books out of 10 (distinct) books?

**Ans. 151200**

How many integers between 100 and 999 inclusive consist of distinct odd digits?

**Ans.** 60

Suppose it is estimated that the chance that A can solve a certain problem is $\frac{2}{3}$ , and the chance that B can solve it is $\frac{5}{12}$ ;let us consider what is the chance of the problem being solved when they both try.

**Ans.** $\frac{29}{36}$

$\int \! \frac{x^{2}}{\sqrt[4]{x^{3}+2}} \, \mathrm{d} x$

**Ans **$\frac{4}{9}({x^{3}+2})^{\frac{3}{4}}+C$

$\int \! \frac{1}{e^{x}+1} \, \mathrm{d} x$

**Ans: **$x-\ln|e^{x}+1|)+C$

$\int \! \frac{(1+x)^{2}}{\sqrt{x}} \, \mathrm{d} x$

**Ans **$2x^{\frac{1}{2}}+\frac{4}{3}x^{\frac{3}{2}}+\frac{2}{5}x^{\frac{5}{2}}+C$

$\int \! \frac{x^{3}}{x+1} \, \mathrm{d} x$

Answer $\frac{x^{3}}{3}-\frac{x^{2}}{2}+x-\ln(x+1)+C$

Answer $\frac{x^{3}}{3}-\frac{x^{2}}{2}+x-\ln(x+1)+C$

$\int \! \frac{2x-1}{2x+3} \, \mathrm{d} x$

Answer $x-2\ln(2x+3)+C$

Answer $x-2\ln(2x+3)+C$

$\int \! \frac{1}{x^{3}} \, \mathrm{d} x$

Answer $-\frac{1}{2x^{2}}+C$

Answer $-\frac{1}{2x^{2}}+C$

$ \lim_{x \to \infty} \frac{x^2x^{\frac{1}{2}} -1}{x^{3}+x^{2}-6} $

Answer : 0

Answer : 0

$ \lim_{x \to 3} \frac{6-\frac{18}{x}}{x-3} $

Answer : 2

Answer : 2

$ \lim_{x \to 3} \frac{x^2 -9}{2x-6} $

Answer : 3

Answer : 3

The mean length of life of a certain tool is 41.5 hours with a standard deviation of 2.5 hours. What is the probability that a simple random sample of size 50 drawn from this population will have a mean of between 40.5 and 42 hours ?

Answer : $0.9215$

Answer : $0.9215$

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