How many 3-digit numbers can be formed using three distinct single digit prime numbers?
Apply the permutation/counting formula directly to the set of usable digits.
The set of usable digits is {2, 3, 5, 7}, a set of size n = 4, since these are exactly the primes less than 10.
Each of the three positions in the 3-digit number is filled independently from this set of 4 digits, giving a total count of 4 x 4 x 4 = 4^3 = 64. Since every digit in {2,3,5,7} is nonzero, all 64 combinations are valid 3-digit numbers with no leading-zero issue.
Final answer: 64.
A student needs to enroll for a minimum of 60 credits. A student cannot enroll for
more than 70 credits. The credits are divided amongst project and three distinct
sets of courses namely, core courses, specialization courses, and elective courses.
It is compulsory for a student to enroll for exactly 15 credits of core courses and
exactly 20 credits of project. In addition, a student has to enroll for a minimum of
10 credits of specialization courses. The maximum credits of elective courses that
a student can enroll for is ______
For positive real numbers π and πΎ, the function π»πΎ(π) is defined as:
π»πΎ(π) = max(πβπΎ, 0). The max function is defined as:
max(π, π) = {π,
when π> π
π,
when πβ€π
The graph below shows the plot of a function π(π) versus π.
π(π) can be expressed as _____.
The values of Stock A and Stock B on a particular day are Rs. 50 and Rs. 80,
respectively. An investor invests Rs. 100 in Stock A and Rs. 80 in Stock B. He
sells all the stocks the next day when the value of Stock A is Rs. 55 and Stock B
is Rs. 70. The profit made by the investor is Rs. ________