Assignment:
Q1. Twenty five scientists are seeking financial support from the National Science Foundation. Find the number of ways in which the NSF panel can select four of the twenty five submitted proposals ranking them as first second , third , and fourth.
Q2. A basket contains 6 red apples and 9 green apples . A sample of 5 apples is drawn. Find the probability that the sample contains
a. Five red apples?
b. Two red and three green apples?
c. at lest one red apple?
Q3. If two cards are drawn from the standard deck without replacement, find the probability that :
a. The first card is red, and the second is black
b. Both cards are aces
Q4. There are seven cards with digits 0,1, 2, 3, 4, 5, and 6. A child takes four of the cards and places them in some order. What is the probability that he obtains a four-digit number less than 3265?
Provide complete and step by step solution for the question and show calculations and use formulas.