3. (a) How many non-negative integer solutions (x1, x2, x3, x4, x5) are there in each of the following cases (i) satisfying xı+ x2+ X3 + x4 + x5 = 25? (ii) satisfying xı+ x2+ x3+ X4+ x5 = 25, with xị > 7, x2 2 6, x3 > 4 ? (iii) satisfying xị+ x2+ x3 + x4 + x5 (iv) satisfying x1+ x2+ x3+ 4 + x5 < 25? = 25 with xı < 10? (b) What is the probability of getting a sum of 14 when 3 dice are rolled?

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3. (a) How many non-negative integer solutions (x1, x2, x3, x4, x5) are there in each of the
following cases
(i) satisfying x1 + x2 + x3 + x4 + xz = 25?
(ii) satisfying x1+ x2+ x3 + X4 + x5 = 25, with x1 > 7, x2 > 6, x3 > 4 ?
(iii) satisfying xi + x2 + X3 + x4 + x5
(iv) satisfying x1+ x2+ X3 + x4 + x5 < 25?
= 25 with x1 < 10?
(b) What is the probability of getting a sum of 14 when 3 dice are rolled?
Transcribed Image Text:3. (a) How many non-negative integer solutions (x1, x2, x3, x4, x5) are there in each of the following cases (i) satisfying x1 + x2 + x3 + x4 + xz = 25? (ii) satisfying x1+ x2+ x3 + X4 + x5 = 25, with x1 > 7, x2 > 6, x3 > 4 ? (iii) satisfying xi + x2 + X3 + x4 + x5 (iv) satisfying x1+ x2+ X3 + x4 + x5 < 25? = 25 with x1 < 10? (b) What is the probability of getting a sum of 14 when 3 dice are rolled?
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