Question

Ava has 11 shirts and 5 ties in her wardrobe. a) On Friday morning, she picks a shirt and a tie at random from the wardrobe. How many possible combinations are there? b) On Friday evening, she puts the tie back in the wardrobe but not the shirt. On Saturday morning, she picks a shirt and a tie at random from the wardrobe again. How many possible combinations are there now?​

Answer 1

Answer: Here are the solutions to your questions:

a) On Friday morning, Ava can pick a shirt and a tie at random from her wardrobe. Since she has 11 shirts and 5 ties, there are 55 possible combinations of shirts and ties that she can choose from. This is because for each of the 11 shirts, there are 5 different ties that she can pair it with. Therefore, the total number of possible combinations is 11 x 5 = 55.

b) On Friday evening, Ava puts the tie back in the wardrobe but not the shirt. On Saturday morning, she picks a shirt and a tie at random from the wardrobe again. Since she has already picked a tie on Friday morning, there are only 4 ties left in her wardrobe. Therefore, there are 44 possible combinations of shirts and ties that she can choose from on Saturday morning. This is because for each of the 11 shirts, there are only 4 different ties that she can pair it with. Therefore, the total number of possible combinations is 11 x 4 = 44.

I hope this helps!

Answer 2

The number of possible combinations for Ava to pick a shirt and a tie is 55. When the tie is not put back, the number of possible combinations remains the same.

Step-by-step explanation:

To find the number of possible combinations, we can use the concept of the multiplication principle. Since Ava has 11 shirts and 5 ties, the total number of possible combinations is 11 multiplied by 5, which equals 55.

On Saturday morning, Ava puts the tie back in the wardrobe, so now she only needs to pick a shirt. Since she still has 11 shirts, the number of possible combinations remains the same, which is 11.