Problem statementSend feedbackIt is December month of the year. Santa is preparing for Christmas evening and has selected five different gifts. He wants to randomly distribute them among Rohit, Ishita, Karan, and Ria. Santa wants to be fair and find out the probability that each child gets at least one gift. Can you help him find that out?00 : 27 : 420/15 attemptedEndOptions: Pick one correct answer from below13/6417/6415/64None of these
Question
Problem statementSend feedbackIt is December month of the year. Santa is preparing for Christmas evening and has selected five different gifts. He wants to randomly distribute them among Rohit, Ishita, Karan, and Ria. Santa wants to be fair and find out the probability that each child gets at least one gift. Can you help him find that out?00 : 27 : 420/15 attemptedEndOptions: Pick one correct answer from below13/6417/6415/64None of these
Solution
The problem is asking for the probability that each child (Rohit, Ishita, Karan, and Ria) gets at least one gift from Santa, who has five different gifts to distribute.
Step 1: Calculate the total number of ways Santa can distribute the gifts.
Since there are 4 children and 5 gifts, and each gift can go to any child, the total number of ways to distribute the gifts is 4^5 = 1024.
Step 2: Calculate the number of ways to distribute the gifts such that at least one child gets no gift.
If at least one child gets no gift, then the gifts are being distributed among only 3 children. The number of ways to do this is 3^5 = 243. However, there are 4 ways to choose which child gets no gift, so the total number of ways to distribute the gifts such that at least one child gets no gift is 4*243 = 972.
Step 3: Subtract the number of ways to distribute the gifts such that at least one child gets no gift from the total number of ways to distribute the gifts.
This gives the number of ways to distribute the gifts such that each child gets at least one gift: 1024 - 972 = 52.
Step 4: Calculate the probability that each child gets at least one gift.
The probability is the number of ways to distribute the gifts such that each child gets at least one gift divided by the total number of ways to distribute the gifts: 52/1024 = 13/256.
So, the correct answer is "None of these".
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