QuestionAugust 25, 2025

There are 50 students at a meeting. They each give out 45 Valentine's out How many different groups of people could they give out the cards.

There are 50 students at a meeting. They each give out 45 Valentine's out How many different groups of people could they give out the cards.
There are 50 students at a meeting. They each give out 45 Valentine's out How many different groups of people could they give out the cards.

Solution
4.7(302 votes)

Answer

211876 Explanation 1. Calculate Total Cards Given Each student gives out 45 cards. Therefore, the total number of cards given is 50 \times 45 = 2250. 2. Determine Unique Groups Each card is given to a different person. Since there are 50 students, each student can give cards to 49 others (excluding themselves). 3. Calculate Combinations The number of ways to choose 45 recipients from 49 possible people is given by the combination formula **C(n, k) = \frac{n!}{k!(n-k)!}** where n = 49 and k = 45. Simplifying, C(49, 45) = C(49, 4) due to symmetry in combinations. C(49, 4) = \frac{49 \times 48 \times 47 \times 46}{4 \times 3 \times 2 \times 1} = 211876.

Explanation

1. Calculate Total Cards Given<br /> Each student gives out 45 cards. Therefore, the total number of cards given is $50 \times 45 = 2250$.<br />2. Determine Unique Groups<br /> Each card is given to a different person. Since there are 50 students, each student can give cards to 49 others (excluding themselves).<br />3. Calculate Combinations<br /> The number of ways to choose 45 recipients from 49 possible people is given by the combination formula **$C(n, k) = \frac{n!}{k!(n-k)!}$** where $n = 49$ and $k = 45$. <br /> Simplifying, $C(49, 45) = C(49, 4)$ due to symmetry in combinations.<br /> $C(49, 4) = \frac{49 \times 48 \times 47 \times 46}{4 \times 3 \times 2 \times 1} = 211876$.
Click to rate:

Similar Questions