How many integral solutions are there to x + y + z + w = 29, where x ≥ 1, y ≥ 2, z ≥ 3 and w ≥ 0?
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: B. 2600
Explanation
Substitute x′ = x − 1, y′ = y − 2, z′ = z − 3: x′ + y′ + z′ + w = 23 with all ≥ 0. The count is C(23 + 3, 3) = C(26, 3) = 2600.More Discrete Structures and Optimisation questions
- In a multi-user operating system, on average 20 requests are made to use a particular resource per hour. The probability that no request is…
- Let G = R \ {0} (non-zero reals) and H = {−1, 1} be groups under multiplication. Then the map φ : G → H defined by φ(x) = x/|x| is
- Find the sum of all four-digit numbers formed using the digits 1, 2, 4 and 6 (each used once).
- Match List I with List IIList I List II A. A △ B I. (A − B) ∪ (A − C) B. A − (B ∪ C) II. (A − B) ∩ (A − C) C. A − (B ∩ C) III. (A − B) ∪ (B…
- Consider the following statements: A. The identity is unique in any monoid. B. A monoid is a group if every element of the monoid has an in…
- If A = {4n + 2 | n is a natural number} and B = {3n | n is a natural number}, which of the following is correct for A ∩ B?