How many three-symbol codes can be formed from the letters I,S,P, and Y without repetition?
4*3*2 = 24
I S P
I S Y
I P S
I P Y
I Y S
I Y P
S I P
S I Y
S P I
S P Y
S Y I
S Y P
P I S
P I Y
P S I
P S Y
P Y I
P Y S
Y I S
Y I P
Y S I
Y S P
Y P I
Y P S
To find the number of three-symbol codes that can be formed from the letters I, S, P, and Y without repetition, you can use the concept of combinations.
Since there are four letters to choose from, you can construct a three-symbol code by selecting three letters from the available options without repetition.
To calculate the number of combinations, you can use the formula for combinations:
C(n, r) = n! / (r!(n - r)!)
Where:
- n is the total number of items (in this case, the number of letters available)
- r is the number of items to be chosen (in this case, the number of symbols in the code)
Using this formula, let's calculate the number of three-symbol codes:
C(4, 3) = 4! / (3!(4 - 3)!)
= 4! / (3! * 1!)
= (4 * 3 * 2 * 1) / (3 * 2 * 1 * 1)
= 4
Therefore, there are four different three-symbol codes that can be formed from the letters I, S, P, and Y without repetition.