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Math  /  Data & Statistics

Question4.) Mary writes each letter of the state TEXAS on a separate card. She randomly picks 5 cards and places them on the table in the order she picks them. What is the probability she gets them in the right order to spell Texas correctly?

Studdy Solution

STEP 1

1. The word "TEXAS" consists of 5 unique letters: T, E, X, A, S.
2. Mary picks all 5 cards and arranges them in a sequence.
3. Each arrangement of the 5 cards is equally likely.

STEP 2

1. Calculate the total number of possible arrangements of the 5 cards.
2. Determine the number of successful outcomes (arrangements that spell "TEXAS").
3. Calculate the probability of the successful arrangement.

STEP 3

Calculate the total number of possible arrangements of the 5 cards. Since each card is unique, the number of permutations of 5 distinct cards is given by 5!5!.
5!=5×4×3×2×1=120 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120

STEP 4

Determine the number of successful outcomes. There is only one correct arrangement that spells "TEXAS".
Number of successful outcomes=1 \text{Number of successful outcomes} = 1

STEP 5

Calculate the probability of picking the cards in the correct order to spell "TEXAS". This is the ratio of successful outcomes to the total number of possible arrangements.
Probability=Number of successful outcomesTotal number of arrangements=1120 \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of arrangements}} = \frac{1}{120}
The probability that Mary picks the cards in the correct order to spell "TEXAS" is:
1120 \boxed{\frac{1}{120}}

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