Let's break down the problem step-by-step to find out how many different ways Sheela can go to the party.
Problem Summary:
- Sheela can choose to go to the party with any subset of her 7 friends: Yogesh, Nikhilesh, Shashank, Amol, Shainu, Vivek, Girish.
- She has 10 pairs of sandals and 17 different dresses.
- She likes only 7 pairs of sandals and 7 dresses that she wants to wear for the party.
- We want to find the total number of different ways she can go to the party, considering:
- The choice of friends she takes along.
- The choice of sandals and dresses she wears.
Step 1: Number of ways to choose friends
She has 7 friends, and she can choose any subset of them to go with her. This includes the possibility of going alone (choosing no friends).
- Number of subsets of a set with 7 elements = 27=1282^7=12827=128
So, there are 128 ways to choose friends.
Step 2: Number of ways to choose sandals and dresses
She wants to wear only from her 7 liked pairs of sandals and 7 liked dresses.
- Number of ways to choose sandals = 7
- Number of ways to choose dresses = 7
Total ways to choose sandals and dresses = 7×7=497\times 7=497×7=49
Step 3: Total number of ways
Total ways = (Number of ways to choose friends) × (Number of ways to choose sandals and dresses)
=128×49=6272=128\times 49=6272=128×49=6272
Final answer:
Sheela can go to the party in 6,272 different ways considering her choice of friends, sandals, and dresses. If you want, I can also help you with variations or more detailed explanations!
