Question

What is the probability that k is the smallest integer in a subset of four different numbers chosen from 1 through 20 (1 ≤ k ≤ 17)?

Answer 1

Hello,

p=4845/116280=0.041666....
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DIM k AS INTEGER, nFav AS LONG, nTot AS LONG, a AS INTEGER, b AS INTEGER, c AS INTEGER, d AS INTEGER
nTot = 0
nFav = 0
FOR k = 1 TO 17
    FOR a = k + 1 TO 18
        FOR b = a + 1 TO 19
            FOR c = b + 1 TO 20
                nFav = nFav + 1
                PRINT nFav; k; a; b; c
            NEXT c
        NEXT b
    NEXT a
NEXT k
nTot = 0
FOR a = 1 TO 20
    FOR b = 1 TO 20
        IF b <> a THEN
            FOR c = 1 TO 20
                IF c <> b AND c <> a THEN
                    FOR d = 1 TO 20
                        IF d <> c AND d <> b AND d <> a THEN
                            nTot = nTot + 1
                            PRINT nTot; a; b; c; d

                        END IF
                    NEXT d
                END IF
            NEXT c
        END IF
    NEXT b
NEXT a
PRINT "nFav="; nFav, "nTot="; nTot, "prob="; nFav / nTot
END