## 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.

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## 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.