# Readers ask: How many different ways can a family visit philadelphia, baltimore, and washington?

## How many different ways could Eight students sit in a semicircle to watch an experiment?

To answer this you need to do the factorial for 8 which is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 and you’ll get the number of combinations that is 40,320 because that’s the **possible** number of combinations.

## How many different ways could a baking contest be judged if 15 pies are entered and 4 ribbons are awarded?

There are **1365 ways** a baking contest ways can be judged if 4 ribbons are awarded with 15 pie entries.

## How many permutations exist of the letters ABCD taken four at a time?

r = Number of objects **taken** at a **time**. We can see total number of **letters** is 4 and number of **letters taken** at a **time** is also 4, so substituting these values in **permutation** formula we will get, Therefore, 24 **permutations exist** for our given **letters** and option A is the correct choices.

## How many permutations exist of the letters A B C D taken three at a time?

There are four **letters a, b**, **c**, **d** and we have to tell the **permutations** made when **taken** 3 at a **time**. Therefore, option (A) 24 are the **permutations exist**.

## How many permutations exist of the letters P Q R S and T taking four at a time?

**P** (n,**r**) = n! / (n-r)! Therefore, there are 120 **permutations exist of the letters p**, **q**, **r**, **s, and t**, **taking four at a time**.

## How many different ways could seven birds perch around a circular bird bath?

Total number of ways = (7-1)! ⇒ 6! Hence, **720 ways** could seven birds perch around a circular bird bath.

## How many ways can ABCD be arranged?

⇒ Total possible arrangement of letters a b c d is **24**.

## How many permutations are there in ABCD?

**ABCD** is the same as ACBD when counting **combinations**. The number of **permutations** with no repeats is 4 x 3 x 2 x 1 = 24 **Permutations**.

## How many permutations are possible with the letters ABC?

Think of the **letters ABC** as glued together. Thus we really have six objects, namely, the super- **letter ABC**, and the individual **letters** D, E, F, G, and H. Because these six objects can occur in any order, **there** are 6! = 720 **permutations** of the **letters** ABCDEFGH in which **ABC** occurs as a block.

## How many permutations exist of the letters ABCD taken two at a time?

Step-by-step explanation: We are given to find the number of **permutations** that **exists** for the **letters** a, b, c and d taking **two at a time**. n = 4 and r = **2**. Thus, there are 12 **permutations** that **exists**. Option (a) is correct.