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← JEE Main 2022 · 27 Jun · Shift 2
MathematicsInteger+4 / -1Question 23 of 90

JEE Main 2022 · 27 Jun · Shift 2, Mathematics question 23

Let A be a matrix of order 2×22\times2, whose entries are from the set {0,1,2,3,4,5}\{0,1,2,3,4,5\}. If the sum of all the entries of A is a prime number pp, 2<p<82<p<8, then the number of such matrices A is ______.

Answer and worked solution

Official answer: 180

Count 4-tuples from {0,…,5}\{0,\dots,5\} with sum 3, 5 or 7 (by stars and bars with the cap 5): 20+56+104=18020+56+104=180.

Answer: 180